{"id":36909,"date":"2022-04-05T11:26:48","date_gmt":"2022-04-05T05:56:48","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=36909"},"modified":"2022-04-07T11:39:49","modified_gmt":"2022-04-07T06:09:49","slug":"big-ideas-math-algebra-1-answers-chapter-5","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers-chapter-5\/","title":{"rendered":"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations"},"content":{"rendered":"<p>Want to become Math Proficient in the future? Then, practice the questions of Ch 5 Solving Systems of Linear Equations from the BIM Algebra 1 Solution Key is the best choice. Also, kids can move on the right track by solving the textbook questions covered in <strong><a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers\/\">Big Ideas Math Algebra 1 Answers<\/a> Chapter 5 Solving Systems of Linear Equations Pdf<\/strong>. Students can also make use of this guide for homework &amp; assignment help.<\/p>\n<p>Moreover, <strong>Ch 5 BIM Math Book Algebra 1 Answers<\/strong> help you to gain a deeper knowledge about the concepts of Solving Systems of Linear Equations &amp; secure high marks in the examinations. Access the Big Ideas Math Book Algebra 1 Chapter 5 Solving Systems of Linear Equations Answer key Topicwise and download them for free &amp; prepare very well.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations<\/h2>\n<p>Here is the complete list of topic-wise Big Ideas Math Book Algebra 1 Chapter 5 Solving Systems of Linear Equations Solution Key which covers the questions from the BIM Textbooks based on the latest Common Core Curriculum. <strong>Ch 5 Big Ideas Math Textbook Algebra 1 Answers<\/strong> material given here offers Questions from Exercises(5.1 to 5.7), Chapter Tests, Review Tests, Quiz, Assessment Tests, Cumulative Assessments, etc. Practice thoroughly and gain more subject knowledge on the concepts of BIM Math Book Algebra 1 Chapter 5 Solutions.<\/p>\n<ul>\n<li style=\"list-style-type: none;\">\n<ul>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_Maintaining_Mathematical_Proficiency\">Solving Systems of Linear Equations Maintaining Mathematical Proficiency &#8211; Page 233<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_Mathematical_Practices\">Solving Systems of Linear Equations Mathematical Practices &#8211; Page 234<\/a><\/li>\n<li><a href=\"#Lesson_5.1_Solving_Systems_of_Linear_Equations_by_Graphing\">Lesson 5.1 Solving Systems of Linear Equations by Graphing &#8211; Page(235-240)<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_by_Graphing_5.1_Exercises\">Solving Systems of Linear Equations by Graphing 5.1 Exercises &#8211; Page(239-240)<\/a><\/li>\n<li><a href=\"#Lesson_5.2_Solving_Systems_of_Linear_Equations_by_Substitution\">Lesson 5.2 Solving Systems of Linear Equations by Substitution &#8211; Page(241-246)<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_by_Substitution_5.2_Exercises\">Solving Systems of Linear Equations by Substitution 5.2 Exercises &#8211; Page(245-246)<\/a><\/li>\n<li><a href=\"#Lesson_5.3_Solving_Systems_of_Linear_Equations_by_Elimination\">Lesson 5.3 Solving Systems of Linear Equations by Elimination &#8211; Page(247-252)<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_by_Elimination_5.3_Exercises\">Solving Systems of Linear Equations by Elimination 5.3 Exercises &#8211; Page(251-252)<\/a><\/li>\n<li><a href=\"#Lesson_5.4_Solving_Special_Systems_of_Linear_Equations\">Lesson 5.4 Solving Special Systems of Linear Equations &#8211; Page(253-258)<\/a><\/li>\n<li><a href=\"#Solving_Special_Systems_of_Linear_Equations_5.4_Exercises\">Solving Special Systems of Linear Equations 5.4 Exercises &#8211; Page(257-258)<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_Study_Skills:_Analyzing_Your_Errors\">Solving Systems of Linear Equations Study Skills: Analyzing Your Errors &#8211; Page 259<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_5.1\u20135.4_Quiz\">Solving Systems of Linear Equations 5.1\u20135.4 Quiz &#8211; Page 260<\/a><\/li>\n<li><a href=\"#Lesson_5.5_Solving_Equations_by_Graphing\">Lesson 5.5 Solving Equations by Graphing &#8211; Page(261-266)<\/a><\/li>\n<li><a href=\"#Solving_Equations_by_Graphing_5.5_Exercises\">Solving Equations by Graphing 5.5 Exercises &#8211; Page(265-266)<\/a><\/li>\n<li><a href=\"#Lesson_5.6_Graphing_Linear_Inequalities_in_Two_Variables\">Lesson 5.6 Graphing Linear Inequalities in Two Variables &#8211; Page(267-272)<\/a><\/li>\n<li><a href=\"#Graphing_Linear_Inequalities_in_Two_Variables_5.6_Exercises\">Graphing Linear Inequalities in Two Variables 5.6 Exercises &#8211; Page(271-272)<\/a><\/li>\n<li><a href=\"#Lesson_5.7_Systems_of_Linear_Inequalities\">Lesson 5.7 Systems of Linear Inequalities &#8211; Page(273-280)<\/a><\/li>\n<li><a href=\"#Systems_of_Linear_Inequalities_5.7_Exercises\">Systems of Linear Inequalities 5.7 Exercises &#8211; Page(278-280)<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_Performance_Task:_Prize_Patrol\">Solving Systems of Linear Equations Performance Task: Prize Patrol &#8211; Page 281<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_Chapter_Review\">Solving Systems of Linear Equations Chapter Review &#8211; Page(282-284)<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_Chapter_Test\">Solving Systems of Linear Equations Chapter Test &#8211; Page 285<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_Cumulative_Assessment\">Solving Systems of Linear Equations Cumulative Assessment &#8211; Page(286-287)<\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_Maintaining_Mathematical_Proficiency\"><\/a>Solving Systems of Linear Equations Maintaining Mathematical Proficiency<\/h3>\n<p><strong>Graph the equation.<\/strong><br \/>\nQuestion 1.<br \/>\ny + 4 = x<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n6x &#8211; y = -1<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n4x + 5y = 20<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n-2y + 12 = -3x<br \/>\nAnswer:<\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><br \/>\nQuestion 5.<br \/>\nm + 4 &gt; 9<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n24 \u2264 -6t<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n2a &#8211; 5 \u2264 13<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n-5z + 1 &lt; -14<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n4k &#8211; 16 &lt; k + 2<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n7w + 12 \u2265 2w &#8211; 3<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nThe graphs of the linear functions g and h have different slopes. The value of both functions at x = a is b. When g and h are graphed in the same coordinate plane, what happens at the point (a, b)?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_Mathematical_Practices\"><\/a>Solving Systems of Linear Equations Mathematical Practices<\/h3>\n<p>Mathematically proficient students use technological tools to explore concepts.<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p>Use a graphing calculator to find the point of intersection of the graphs of the two linear equations.<br \/>\nQuestion 1.<br \/>\ny = -2x &#8211; 3<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 3<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ny = -x + 1<br \/>\ny = x- 2<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n3x &#8211; 2y = 2<br \/>\n2x &#8211; y = 2<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.1_Solving_Systems_of_Linear_Equations_by_Graphing\"><\/a>Lesson 5.1 Solving Systems of Linear Equations by Graphing<\/h3>\n<p><strong>Essential Question<\/strong> How can you solve a system of linear equations?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing a System of Linear EquationsWork with a partner. Your family opens a bed-and-breakfast. They spend $600 preparing a bedroom to rent. The cost to your family for food and utilities is $15 per night. They charge $75 per night to rent the bedroom.<br \/>\na. Write an equation that represents the costs.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 1\" width=\"295\" height=\"51\" \/><br \/>\nb. Write an equation that represents the revenue (income).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 2\" width=\"279\" height=\"49\" \/><br \/>\nc. A set of two (or more) linear equations is called a system of linear equations. Write the system of linear equations for this problem.<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Using a Table or Graph to Solve a System<br \/>\nWork with a partner. Use the cost and revenue equations from Exploration 1 to determine how many nights your family needs to rent the bedroom before recovering the cost of preparing the bedroom. This is the break-even point.<br \/>\na. Copy and complete the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 3\" width=\"737\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-3.png 737w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-3-300x90.png 300w\" sizes=\"(max-width: 737px) 100vw, 737px\" \/><br \/>\nb. How many nights does your family need to rent the bedroom before breaking even?<br \/>\nc. In the same coordinate plane, graph the cost equation and the revenue equation from Exploration 1.<br \/>\nd. Find the point of intersection of the two graphs. What does this point represent? How does this compare to the break-even point in part (b)? Explain.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you solve a system of linear equations? How can you check your solution?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nSolve each system by using a table or sketching a graph. Explain why you chose each method. Use a graphing calculator to check each solution.<br \/>\na. y = -4.3x &#8211; 1.3<br \/>\ny = 1.7x + 4.7<\/p>\n<p>b. y = x<br \/>\ny = -3x + 8<\/p>\n<p>c. y = -x &#8211; 1<br \/>\ny = 3x + 5<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Tell whether the ordered pair is a solution of the system of linear equations.<\/strong><br \/>\nQuestion 1.<br \/>\n(1, -2); 2x + y = 0<br \/>\n-x + 2y = 5<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n(1, 4); y = 3x + 1<br \/>\ny = -x + 5<br \/>\nAnswer:<\/p>\n<p><strong>Solve the system of linear equations by graphing.<\/strong><br \/>\nQuestion 3.<br \/>\ny = x &#8211; 2<br \/>\ny = -x + 4<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\ny = \\(\\frac{1}{2}\\)x + 3<br \/>\ny = &#8211;\\(\\frac{3}{2}\\)x &#8211; 5<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n2x + y = 5<br \/>\n3x &#8211; 2y = 4<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nYou have a total of 18 math and science exercises for homework. You have six more math exercises than science exercises. How many exercises do you have in each subject?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_by_Graphing_5.1_Exercises\"><\/a>Solving Systems of Linear Equations by Graphing 5.1 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nDo the equations 5y &#8211; 2x = 18 and 6x = -4y &#8211; 10 form a system of linear equations? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44771\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 1\" width=\"565\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-1.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-1-300x45.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nConsider the system of linear equations -4x + 2y = 4 and 4x &#8211; y = -6. Which is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-4.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 4\" width=\"523\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-4.png 523w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-4-300x52.png 300w\" sizes=\"(max-width: 523px) 100vw, 523px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20138, tell whether the ordered pair is a solution of the system of linear equations.<\/strong><br \/>\nQuestion 3.<br \/>\n(2, 6); x + y = 8<br \/>\n3x &#8211; y = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44772\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 3\" width=\"568\" height=\"262\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-3.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-3-300x138.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 4.<br \/>\n(8, 2); x &#8211; y = 6<br \/>\n2x &#8211; 10y = 4<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n(-1, 3); y = -7x &#8211; 4<br \/>\ny = 8x + 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44773\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 5\" width=\"577\" height=\"286\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-5.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-5-300x149.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 6.<br \/>\n(-4, -2); y = 2x + 6<br \/>\ny = -3x &#8211; 14<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n(-2, 1); 6x + 5y = -7<br \/>\n2x &#8211; 4y = -8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44774\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 7\" width=\"515\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-7.png 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-7-300x151.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p>Question 8.<br \/>\n(5, -6); 6x + 3y = 12<br \/>\n4x + y = 14<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 9\u201312, use the graph to solve the system of linear equations. Check your solution.<\/strong><br \/>\nQuestion 9.<br \/>\nx &#8211; y = 4<br \/>\n4x + y = 1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 5\" width=\"131\" height=\"127\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44775\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 9\" width=\"473\" height=\"269\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-9.png 473w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-9-300x171.png 300w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><\/p>\n<p>Question 10.<br \/>\nx + y = 5<br \/>\ny &#8211; 2x = -4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-6.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 6\" width=\"127\" height=\"125\" \/><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n6y + 3x = 18<br \/>\n-x + 2y = 24<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 7\" width=\"136\" height=\"130\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44776\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 11\" width=\"537\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-11.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-11-300x145.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 12.<br \/>\n2x &#8211; y = -2<br \/>\n2x + 4y = 8<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-8.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 8\" width=\"135\" height=\"131\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 13\u201320, solve the system of linear equations by graphing.<\/strong><br \/>\nQuestion 13.<br \/>\ny = -x + 7<br \/>\ny = x + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44777\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 13\" width=\"384\" height=\"431\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-13.png 384w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-13-267x300.png 267w\" sizes=\"(max-width: 384px) 100vw, 384px\" \/><\/p>\n<p>Question 14.<br \/>\ny = -x + 4<br \/>\ny = 2x &#8211; 8<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\ny = \\(\\frac{1}{3}\\)x + 2<br \/>\ny = \\(\\frac{2}{3}\\)x + 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44778\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 15\" width=\"474\" height=\"484\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-15.png 474w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-15-294x300.png 294w\" sizes=\"(max-width: 474px) 100vw, 474px\" \/><\/p>\n<p>Question 16.<br \/>\ny = \\(\\frac{3}{4}\\)x &#8211; 4<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x + 11<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n9x + 3y = -3<br \/>\n2x &#8211; y = -4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44779\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-17.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 17.1\" width=\"574\" height=\"465\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-17.1.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-17.1-300x243.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44780\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-17.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 17.2\" width=\"522\" height=\"244\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-17.2.png 522w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-17.2-300x140.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/p>\n<p>Question 18.<br \/>\n4x &#8211; 4y = 20<br \/>\ny = -5<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nx &#8211; 4y = -4<br \/>\n-3x &#8211; 4y = 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44781\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-19.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 19.1\" width=\"532\" height=\"469\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-19.1.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-19.1-300x264.png 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44782\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-19.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 19.2\" width=\"572\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-19.2.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-19.2-300x129.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 20.<br \/>\n3y + 4x = 3<br \/>\nx + 3y = -6<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 21 and 22, describe and correct the error in solving the system of linear equations.<br \/>\nQuestion 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 9\" width=\"335\" height=\"151\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-9.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-9-300x135.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44783\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-21.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 21.1\" width=\"591\" height=\"526\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-21.1.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-21.1-300x267.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44784\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-21.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 21.2\" width=\"583\" height=\"269\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-21.2.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-21.2-300x138.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-10.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 10\" width=\"334\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-10.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-10-300x141.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>USING TOOLS<\/strong> In Exercises 23\u201326, use a graphing calculator to solve the system of linear equations.<br \/>\nQuestion 23.<br \/>\n0.2x + 0.4y = 4<br \/>\n-0.6x + 0.6y = -3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44785\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 23\" width=\"377\" height=\"612\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-23.png 377w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-23-185x300.png 185w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><\/p>\n<p>Question 24.<br \/>\n-1.6x &#8211; 3.2y = -24<br \/>\n2.6x + 2.6y = 26<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n-7x + 6y = 0<br \/>\n0.5x + y = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44786\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 25\" width=\"576\" height=\"307\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-25.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-25-300x160.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 26.<br \/>\n4x &#8211; y = 1.5<br \/>\n2x + y = 1.5<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou have 40 minutes to exercise at the gym, and you want to burn 300 calories total using both machines. How much time should you spend on each machine?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 11\" width=\"255\" height=\"182\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44787\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-27.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 27.1\" width=\"584\" height=\"247\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-27.1.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-27.1-300x127.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44788\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-27.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 27.2\" width=\"598\" height=\"480\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-27.2.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-27.2-300x241.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44789\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-27.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 27.3\" width=\"575\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-27.3.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-27.3-300x143.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou sell small and large candles at a craft fair. You collect $144 selling a total of 28 candles. How many of each type of candle did you sell?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-12.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 12\" width=\"128\" height=\"134\" \/><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nWrite a linear equation that represents the area and a linear equation that represents the perimeter of the rectangle. Solve the system of linear equations by graphing. Interpret your solution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 13\" width=\"213\" height=\"79\" \/><br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-44790\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-29.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 29.1\" width=\"524\" height=\"437\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-29.1.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-29.1-300x250.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44791\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-29.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 29.2\" width=\"531\" height=\"308\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-29.2.png 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-29.2-300x174.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nYour friend\u2019s bank account balance (in dollars) is represented by the equation y = 25x + 250, where x is the number of months. Graph this equation. After 6 months, you want to have the same account balance as your friend. Write a linear equation that represents your account balance. Interpret the slope and y-intercept of the line that represents your account balance.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nConsider the equation x + 2 = 3x &#8211; 4.<br \/>\na. Solve the equation using algebra.<br \/>\nb. Solve the system of linear equations y = x + 2 and y = 3x &#8211; 4 by graphing.<br \/>\nc. How is the linear system and the solution in part (b) related to the original equation and the solution in part (a)?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44792\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-31.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 31.1\" width=\"308\" height=\"546\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-31.1.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-31.1-169x300.png 169w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44793\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-31.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 31.2\" width=\"581\" height=\"408\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-31.2.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-31.2-300x211.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nA teacher is purchasing binders for students. The graph shows the total costs of ordering x binders from three different companies.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-14.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 14\" width=\"229\" height=\"186\" \/><br \/>\na. For what numbers of binders are the costs the same at two different companies? Explain.<br \/>\nb. How do your answers in part (a) relate to systems of linear equations?<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYou and a friend are going hiking but start at different locations. You start at the trailhead and walk 5 miles per hour. Your friend starts 3 miles from the trailhead and walks 3 miles per hour.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.1 15\" width=\"185\" height=\"159\" \/><br \/>\na. Write and graph a system of linear equations that represents this situation.<br \/>\nb. Your friend says that after an hour of hiking you will both be at the same location on the trail. Is your friend correct? Use the graph from part (a) to explain your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44794\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-33.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 33.1\" width=\"576\" height=\"445\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-33.1.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-33.1-300x232.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44795\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-33.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 33.2\" width=\"584\" height=\"168\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-33.2.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-33.2-300x86.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Solve the literal equation for y.<\/strong><br \/>\nQuestion 34.<br \/>\n10x + 5y = 5x + 20<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n9x + 18 = 6y &#8211; 3x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44796\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.1 Question 35\" width=\"417\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-35.png 417w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.1-Question-35-300x167.png 300w\" sizes=\"(max-width: 417px) 100vw, 417px\" \/><\/p>\n<p>Question 36.<br \/>\n\\(\\frac{3}{4}\\) x + \\(\\frac{1}{4}\\) y = 5<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.2_Solving_Systems_of_Linear_Equations_by_Substitution\"><\/a>Lesson 5.2 Solving Systems of Linear Equations by Substitution<\/h3>\n<p><strong>Essential Question<\/strong> How can you use substitution to solve a system of linear equations?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using Substitution to Solve Systems<br \/>\nWork with a partner. Solve each system of linear equations using two methods.<br \/>\nMethod 1 Solve for x first.<br \/>\nSolve for x in one of the equations. Substitute the expression for x into the other equation to find y. Then substitute the value of y into one of the original equations to find x.<\/p>\n<p>Method 2 Solve for y first.<br \/>\nSolve for y in one of the equations. Substitute the expression for y into the other equation to find x. Then substitute the value of x into one of the original equations to find y.<br \/>\nIs the solution the same using both methods? Explain which method you would prefer to use for each system<br \/>\na. x + y = -7<br \/>\n-5x + y = 5<\/p>\n<p>b. x &#8211; 6y = -11<br \/>\n3x + 2y = 7<\/p>\n<p>c. 4x + y = -1<br \/>\n3x &#8211; 5y = -18<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Writing and Solving a System of Equations<br \/>\nWork with a partner.<br \/>\na. Write a random ordered pair with integer coordinates. One way to do this is to use a graphing calculator. The ordered pair generated at the right is (-2, -3).<br \/>\nb. Write a system of linear equations that has your ordered pair as its solution.<br \/>\nc. Exchange systems with your partner and use one of the methods from Exploration 1 to solve the system. Explain your choice of method.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 1\" width=\"425\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-1.png 425w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-1-300x142.png 300w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you use substitution to solve a system of linear equations?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nUse one of the methods from Exploration 1 to solve each system of linear equations. Explain your choice of method. Check your solutions.<br \/>\na. x + 2y = -7<br \/>\n2x &#8211; y = -9<\/p>\n<p>b.x &#8211; 2y = -6<br \/>\n2x + y = -2<\/p>\n<p>c.-3x + 2y = -10<br \/>\n-2x + y = -6<\/p>\n<p>d. 3x + 2y = 13<br \/>\nx &#8211; 3y = -3<\/p>\n<p>e. 3x &#8211; 2y = 9<br \/>\n-x &#8211; 3y = 8<\/p>\n<p>f. 3x &#8211; y = -6<br \/>\n4x + 5y = 11<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the system of linear equations by substitution. Check your solution.<\/strong><br \/>\nQuestion 1.<br \/>\ny = 3x + 14<br \/>\ny = -4x<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n3x + 2y = 0<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 1<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nx = 6y &#8211; 7<br \/>\n4x + y = -3<br \/>\nAnswer:<\/p>\n<p><strong>Solve the system of linear equations by substitution. Check your solution.<\/strong><br \/>\nQuestion 4.<br \/>\nx + y = -2<br \/>\n-3x + y = 6<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n-x + y = -4<br \/>\n4x &#8211; y = 10<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n2x &#8211; y = -5<br \/>\n3x &#8211; y = 1<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nx &#8211; 2y = 7<br \/>\n3x &#8211; 2y = 3<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nThere are a total of 64 students in a drama club and a yearbook club. The drama club has 10 more students than the yearbook club. Write a system of linear equations that represents this situation. How many students are in each club?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_by_Substitution_5.2_Exercises\"><\/a>Solving Systems of Linear Equations by Substitution 5.2 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe how to solve a system of linear equations by substitution.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44797\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 1\" width=\"575\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-1.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-1-300x87.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nWhen solving a system of linear equations by substitution, how do you decide which variable to solve for in Step 1?<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u22128, tell which equation you would choose to solve for one of the variables. Explain.<\/strong><br \/>\nQuestion 3.<br \/>\nx + 4y = 30<br \/>\nx &#8211; 2y = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44798\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 3\" width=\"514\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-3.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-3-300x34.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 4.<br \/>\n3x &#8211; y = 0<br \/>\n2x + y = -10<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n5x + 3y = 11<br \/>\n5x &#8211; y = 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44799\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 5\" width=\"514\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-5.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-5-300x33.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 6.<br \/>\n3x &#8211; 2y = 19<br \/>\nx + y = 8<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nx &#8211; y = -3<br \/>\n4x + 3y = -5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44800\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 7\" width=\"519\" height=\"55\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-7.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-7-300x32.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 8.<br \/>\n3x + 5y = 25<br \/>\nx &#8211; 2y = -6<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 9\u201316, solve the system of linear equations by substitution. Check your solution.<\/strong><br \/>\nQuestion 9.<br \/>\nx = 17 &#8211; 4y<br \/>\ny = x &#8211; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44801\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-9.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 9.1\" width=\"503\" height=\"523\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-9.1.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-9.1-289x300.png 289w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44802\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-9.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 9.2\" width=\"390\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-9.2.png 390w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-9.2-300x158.png 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><\/p>\n<p>Question 10.<br \/>\n6x &#8211; 9 = y<br \/>\ny = -3x<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nx = 16 &#8211; 4y<br \/>\n3x + 4y = 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44803\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-11.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 11.1\" width=\"508\" height=\"537\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-11.1.png 508w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-11.1-284x300.png 284w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44804\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-11.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 11.2\" width=\"468\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-11.2.png 468w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-11.2-300x128.png 300w\" sizes=\"(max-width: 468px) 100vw, 468px\" \/><\/p>\n<p>Question 12.<br \/>\n-5x + 3y = 51<br \/>\ny = 10x &#8211; 8<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n2x = 12<br \/>\nx &#8211; 5y = -29<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44805\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 13\" width=\"451\" height=\"642\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-13.png 451w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-13-211x300.png 211w\" sizes=\"(max-width: 451px) 100vw, 451px\" \/><\/p>\n<p>Question 14.<br \/>\n2x &#8211; y = 23<br \/>\nx &#8211; 9 = -1<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n5x + 2y = 9<br \/>\nx + y = -3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44806\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-15.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 15.1\" width=\"346\" height=\"415\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-15.1.png 346w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-15.1-250x300.png 250w\" sizes=\"(max-width: 346px) 100vw, 346px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44807\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-15.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 15.2\" width=\"518\" height=\"347\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-15.2.png 518w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-15.2-300x201.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/p>\n<p>Question 16.<br \/>\n11x &#8211; 7y = -14<br \/>\nx &#8211; 2y = -4<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving for one of the variables in the linear system 8x + 2y = -12 and 5x &#8211; y = 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 2\" width=\"275\" height=\"155\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44808\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-17.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 17.1\" width=\"544\" height=\"254\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-17.1.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-17.1-300x140.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-17.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 17.2\" width=\"363\" height=\"362\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-17.2.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-17.2-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-17.2-150x150.png 150w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 18.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving for one of the variables in the linear system 4x + 2y = 6 and 3x + y = 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 3\" width=\"295\" height=\"230\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA farmer plants corn and wheat on a 180-acre farm. The farmer wants to plant three times as many acres of corn as wheat. Write a system of linear equations that represents this situation. How many acres of each crop should the farmer plant?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-19.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 19.1\" width=\"547\" height=\"539\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-19.1.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-19.1-300x296.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-19.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 19.2\" width=\"504\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-19.2.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-19.2-300x120.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA company that offers tubing trips down a river rents tubes for a person to use and \u201ccooler\u201d tubes to carry food and water. A group spends $270 to rent a total of 15 tubes. Write a system of linear equations that represents this situation. How many of each type of tube does the group rent?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-4.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 4\" width=\"306\" height=\"131\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-4.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-4-300x128.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 21\u201324, write a system of linear equations that has the ordered pair as its solution.<\/strong><br \/>\nQuestion 21.<br \/>\n(3, 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44812\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 21\" width=\"540\" height=\"432\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-21.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-21-300x240.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 22.<br \/>\n(-2, 8)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n(-4, -12)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 23\" width=\"549\" height=\"471\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-23.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-23-300x257.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 24.<br \/>\n(15, -25)<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-25.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 25.1\" width=\"541\" height=\"493\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-25.1.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-25.1-300x273.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-25.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 25.2\" width=\"580\" height=\"539\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-25.2.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-25.2-300x279.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nAn investor owns shares of Stock A and Stock B. The investor owns a total of 200 shares with a total value of $4000. How many shares of each stock does the investor own?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 5\" width=\"151\" height=\"85\" \/><br \/>\nAnswer:<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong> In Exercises 27 and 28, (a) write an equation that represents the sum of the angle measures of the triangle and (b) use your equation and the equation shown to find the values of x and y.<br \/>\nQuestion 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-6.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 6\" width=\"207\" height=\"97\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-27.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 27.1\" width=\"350\" height=\"473\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-27.1.png 350w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-27.1-222x300.png 222w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-27.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 27.2\" width=\"238\" height=\"209\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 7\" width=\"200\" height=\"118\" \/><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>REASONING<\/strong><br \/>\nFind the values of a and b so that the solution of the linear system is (-9, 1).<br \/>\nax + by = -31 Equation 1<br \/>\nax &#8211; by = -41 Equation 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-29.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 29.1\" width=\"565\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-29.1.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-29.1-300x250.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-29.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 29.2\" width=\"553\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-29.2.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-29.2-300x130.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says that given a linear system with an equation of a horizontal line and an equation of a vertical line, you cannot solve the system by substitution. Is your friend correct? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite a system of linear equations in which (3, -5) is a solution of Equation 1 but not a solution of Equation 2, and (-1, 7) is a solution of the system.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-31.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 31.1\" width=\"615\" height=\"600\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-31.1.png 615w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-31.1-300x293.png 300w\" sizes=\"(max-width: 615px) 100vw, 615px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-31.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 31.2\" width=\"580\" height=\"135\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-31.2.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-31.2-300x70.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graphs of two linear equations are shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-8.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 8\" width=\"170\" height=\"166\" \/><br \/>\na. At what point do the lines appear to intersect?<br \/>\nb. Could you solve a system of linear equations by substitution to check your answer in part (a)? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>REPEATED REASONING<\/strong><br \/>\nA radio station plays a total of 272 pop, rock, and hip-hop songs during a day. The number of pop songs is 3 times the number of rock songs. The number of hip-hop songs is 32 more than the number of rock songs. How many of each type of song does the radio station play?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-33.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 33.1\" width=\"601\" height=\"508\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-33.1.png 601w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-33.1-300x254.png 300w\" sizes=\"(max-width: 601px) 100vw, 601px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-33.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 33.2\" width=\"602\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-33.2.png 602w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-33.2-300x247.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nYou have $2.65 in coins. Write a system of equations that represents this situation. Use variables to represent the number of each type of coin.<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nThe sum of the digits of a two-digit number is 11. When the digits are reversed, the number increases by 27. Find the original number<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-35.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 35.1\" width=\"535\" height=\"465\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-35.1.png 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-35.1-300x261.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-35.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 35.2\" width=\"502\" height=\"589\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-35.2.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-35.2-256x300.png 256w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Find the sum or difference.<\/strong><br \/>\nQuestion 36.<br \/>\n(x &#8211; 4) + (2x &#8211; 7)<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n(5y &#8211; 12) + (-5y &#8211; 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-37.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 37.1\" width=\"431\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-37.1.png 431w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-37.1-300x77.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/p>\n<p>Question 38.<br \/>\n(t &#8211; 8) &#8211; (t + 15)<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n(6d + 2) &#8211; (3d &#8211; 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 39\" width=\"399\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-39.png 399w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-39-300x62.png 300w\" sizes=\"(max-width: 399px) 100vw, 399px\" \/><\/p>\n<p>Question 40.<br \/>\n4(m + 2) + 3(6m &#8211; 4)<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n2(5v + 6) &#8211; 6(-9v + 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.2 Question 41\" width=\"550\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-41.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.2-Question-41-300x75.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<h3><a id=\"Lesson_5.3_Solving_Systems_of_Linear_Equations_by_Elimination\"><\/a>Lesson 5.3 Solving Systems of Linear Equations by Elimination<\/h3>\n<p><strong>Essential Question<\/strong> How can you use elimination to solve a system of linear equations?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing and Solving a System of Equations<br \/>\nWork with a partner. You purchase a drink and a sandwich for $4.50. Your friend purchases a drink and five sandwiches for $16.50. You want to determine the price of a drink and the price of a sandwich.<br \/>\na. Let x represent the price (in dollars) of one drink. Let y represent the price (in dollars) of one sandwich. Write a system of equations for the situation. Use the following verbal model.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36934\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations 5.3 1\" width=\"397\" height=\"47\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-1.png 397w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-1-300x36.png 300w\" sizes=\"(max-width: 397px) 100vw, 397px\" \/><br \/>\nLabel one of the equations Equation 1 and the other equation Equation 2.<br \/>\nb. Subtract Equation 1 from Equation 2. Explain how you can use the result to solve the system of equations. Then find and interpret the solution.<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Using Elimination to Solve Systems<br \/>\nWork with a partner. Solve each system of linear equations using two methods.<br \/>\nMethod 1 Subtract. Subtract Equation 2 from Equation 1. Then use the result to solve the system.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36935\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-2.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations 5.3 2\" width=\"222\" height=\"171\" \/><br \/>\nMethod 2 Add. Add the two equations. Then use the result to solve the system.<br \/>\nIs the solution the same using both methods? Which method do you prefer?<br \/>\na. 3x &#8211; y = 6<br \/>\n3x + y = 0<\/p>\n<p>b. 2x + y = 6<br \/>\n2x &#8211; y = 2<\/p>\n<p>c. x &#8211; 2y = -7<br \/>\nx + 2y = 5<\/p>\n<p><strong>EXPLORATION 3<\/strong><\/p>\n<p>Using Elimination to Solve a System<br \/>\nWork with a partner.<br \/>\n2x + y = 7 Equation 1<br \/>\nx + 5y = 17 Equation 2<br \/>\na. Can you eliminate a variable by adding or subtracting the equations as they are? If not, what do you need to do to one or both equations so that you can?<br \/>\nb. Solve the system individually. Then exchange solutions with your partner and compare and check the solutions.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 4.<br \/>\nHow can you use elimination to solve a system of linear equations?<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nWhen can you add or subtract the equations in a system to solve the system? When do you have to multiply first? Justify your answers with examples.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nIn Exploration 3, why can you multiply an equation in the system by a constant and not change the solution of the system? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the system of linear equations by elimination. Check your solution.<\/strong><br \/>\nQuestion 1.<br \/>\n3x + 2y = 7<br \/>\n-3x + 4y = 5<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nx &#8211; 3y = 24<br \/>\n3x + y = 12<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nx + 4y = 22<br \/>\n4x + y = 13<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nSolve the system in Example 3 by eliminating x.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_by_Elimination_5.3_Exercises\"><\/a>Solving Systems of Linear Equations by Elimination 5.3 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<br \/>\n<\/strong>Question 1.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nGive an example of a system of linear equations that can be solved by first adding the equations to eliminate one variable.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 1\" width=\"572\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-1.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-1-300x61.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to solve the system of linear equations by elimination.<br \/>\n2x &#8211; 3y = -4 Equation 1<br \/>\n-5x + 9y = 7 Equation 2<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u221210, solve the system of linear equations by elimination. Check your solution.<\/strong><br \/>\nQuestion 3.<br \/>\nx + 2y = 13<br \/>\n-x + y = 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-3.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 3.1\" width=\"260\" height=\"476\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-3.1.png 260w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-3.1-164x300.png 164w\" sizes=\"(max-width: 260px) 100vw, 260px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-3.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 3.2\" width=\"473\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-3.2.png 473w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-3.2-300x128.png 300w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><\/p>\n<p>Question 4.<br \/>\n9x + y = 2<br \/>\n-4x &#8211; y = -17<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n5x + 6y = 50<br \/>\nx &#8211; 6y = -26<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-5.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 5.1\" width=\"274\" height=\"514\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-5.1.png 274w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-5.1-160x300.png 160w\" sizes=\"(max-width: 274px) 100vw, 274px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-5.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 5.2\" width=\"511\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-5.2.png 511w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-5.2-300x117.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p>Question 6.<br \/>\n-x + y = 4<br \/>\nx + 3y = 4<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n-3x &#8211; 5y = -7<br \/>\n-4x + 5y = 14<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-7.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 7.1\" width=\"282\" height=\"552\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-7.1.png 282w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-7.1-153x300.png 153w\" sizes=\"(max-width: 282px) 100vw, 282px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-7.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 7.2\" width=\"508\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-7.2.png 508w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-7.2-300x119.png 300w\" sizes=\"(max-width: 508px) 100vw, 508px\" \/><\/p>\n<p>Question 8.<br \/>\n4x &#8211; 9y = -21<br \/>\n-4x &#8211; 3y = 9<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n-y &#8211; 10 = 6x<br \/>\n5x + y = -10<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-9.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 9.1\" width=\"424\" height=\"464\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-9.1.png 424w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-9.1-274x300.png 274w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-9.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 9.2\" width=\"558\" height=\"351\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-9.2.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-9.2-300x189.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 10.<br \/>\n3x &#8211; 30 = y<br \/>\n7y &#8211; 6 = 3x<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 11\u201318, solve the system of linear equations by elimination. Check your solution.<\/strong><br \/>\nQuestion 11.<br \/>\nx + y = 2<br \/>\n2x + 7y = 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-11.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 11.1\" width=\"561\" height=\"636\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-11.1.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-11.1-265x300.png 265w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 12.<br \/>\n8x &#8211; 5y = 11<br \/>\n4x &#8211; 3y = 5<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n11x &#8211; 20y = 28<br \/>\n3x + 4y = 36<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-13.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 13.1\" width=\"514\" height=\"567\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-13.1.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-13.1-272x300.png 272w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-13.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 13.2\" width=\"520\" height=\"212\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-13.2.png 520w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-13.2-300x122.png 300w\" sizes=\"(max-width: 520px) 100vw, 520px\" \/><\/p>\n<p>Question 14.<br \/>\n10x &#8211; 9y = 46<br \/>\n-2x + 3y = 10<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n4x &#8211; 3y = 8<br \/>\n5x &#8211; 2y = -11<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-15.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 15.1\" width=\"542\" height=\"556\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-15.1.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-15.1-292x300.png 292w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-15.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 15.2\" width=\"578\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-15.2.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-15.2-300x106.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 16.<br \/>\n-2x &#8211; 5y = 9<br \/>\n3x + 11y = 4<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n9x + 2y = 39<br \/>\n6x + 13y = -9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-17.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 17.1\" width=\"528\" height=\"579\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-17.1.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-17.1-274x300.png 274w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-17.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 17.2\" width=\"569\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-17.2.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-17.2-300x105.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 18.<br \/>\n12x &#8211; 7y = -2<br \/>\n8x + 11y = 30<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving for one of the variables in the linear system 5x &#8211; 7y = 16 and x + 7y = 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations 5.3 3\" width=\"201\" height=\"114\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 19\" width=\"486\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-19.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-19-300x175.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving for one of the variables in the linear system 4x + 3y = 8 and x &#8211; 2y = -13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-4.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations 5.3 4\" width=\"364\" height=\"166\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-4.png 364w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-4-300x137.png 300w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA service center charges a fee of x dollars for an oil change plus y dollars per quart of oil used. A sample of its sales record is shown. Write a system of linear equations that represents this situation. Find the fee and cost per quart of oil.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations 5.3 5\" width=\"332\" height=\"127\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-5.png 332w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-5-300x115.png 300w\" sizes=\"(max-width: 332px) 100vw, 332px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44846\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-21.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 21.1\" width=\"581\" height=\"488\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-21.1.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-21.1-300x252.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-21.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 21.2\" width=\"557\" height=\"265\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-21.2.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-21.2-300x143.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 22.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA music website charges x dollars for individual songs and y dollars for entire albums. Person A pays $25.92to download 6 individual songs and 2 albums. Person B pays $33.93 to download 4 individual songs and 3 albums. Write a system of linear equations that represents this situation. How much does the website charge to download a song? an entire album?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-6.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations 5.3 6\" width=\"123\" height=\"181\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 23\u201326, solve the system of linear equations using any method. Explain why you chose the method.<\/strong><br \/>\nQuestion 23.<br \/>\n3x + 2y = 4<br \/>\n2y = 8 &#8211; 5x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-23.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 23.1\" width=\"340\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-23.1.png 340w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-23.1-195x300.png 195w\" sizes=\"(max-width: 340px) 100vw, 340px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44849\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-23.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 23.2\" width=\"526\" height=\"314\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-23.2.png 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-23.2-300x179.png 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p>Question 24.<br \/>\n-6y + 2 = -4x<br \/>\ny &#8211; 2 = x<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\ny &#8211; x = 2<br \/>\ny = &#8211; \\(\\frac{1}{4}\\) x + 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44850\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 25\" width=\"586\" height=\"486\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-25.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-25-300x249.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 26.<br \/>\n3x + y = \\(\\frac{1}{3}\\)<br \/>\n2x &#8211; 3y = \\(\\frac{8}{3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>WRITING<\/strong><br \/>\nFor what values of a can you solve the linear system ax + 3y = 2 and 4x + 5y = 6 by elimination without multiplying first? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44851\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 27\" width=\"579\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-27.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-27-300x73.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe circle graph shows the results of a survey in which 50 students were asked about their favorite meal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36940\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-7.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations 5.3 7\" width=\"157\" height=\"181\" \/><br \/>\na. Estimate the numbers of students who chose breakfast and lunch.<br \/>\nb. The number of students who chose lunch was 5 more than the number of students who chose breakfast. Write a system of linear equations that represents the numbers of students who chose breakfast and lunch.<br \/>\nc. Explain how you can solve the linear system in part (b) to check your answers in part (a).<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says that any system of equations that can be solved by elimination can be solved by substitution in an equal or fewer number of steps. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 29\" width=\"564\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-29.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-29-300x105.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nWrite a system of linear equations that can be added to eliminate a variable or subtracted to eliminate a variable.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nA rectangle has a perimeter of 18 inches. A new rectangle is formed by doubling the width w and tripling the length \u2113, as shown. The new rectangle has a perimeter P of 46 inches.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-8.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations 5.3 8\" width=\"179\" height=\"91\" \/><br \/>\na. Write and solve a system of linear equations to find the length and width of the original rectangle.<br \/>\nb. Find the length and width of the new rectangle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-31.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 31.1\" width=\"517\" height=\"334\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-31.1.png 517w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-31.1-300x194.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44854\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-31.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 31.2\" width=\"562\" height=\"404\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-31.2.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-31.2-300x216.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nRefer to the discussion of System 1 and System 2 on page 248. Without solving, explain why the two systems shown have the same solution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-9.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations 5.3 9\" width=\"349\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-9.png 349w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-9-300x60.png 300w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou are making 6 quarts of fruit punch for a party. You have bottles of 100% fruit juice and 20% fruit juice. How many quarts of each type of juice should you mix to make 6 quarts of 80% fruit juice?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-33.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 33.1\" width=\"574\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-33.1.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-33.1-300x274.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-33.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 33.2\" width=\"557\" height=\"372\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-33.2.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-33.2-300x200.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA motorboat takes 40 minutes to travel 20 miles downstream. The return trip takes 60 minutes. What is the speed of the current?<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nSolve for x, y, and z in the system of equations. Explain your steps.<br \/>\nx + 7y + 3z = 29 Equation 1<br \/>\n3z + x &#8211; 2y = -7 Equation 2<br \/>\n5y = 10 &#8211; 2x Equation 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-35.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 35.1\" width=\"411\" height=\"339\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-35.1.png 411w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-35.1-300x247.png 300w\" sizes=\"(max-width: 411px) 100vw, 411px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-35.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 35.2\" width=\"485\" height=\"523\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-35.2.png 485w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-35.2-278x300.png 278w\" sizes=\"(max-width: 485px) 100vw, 485px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-35.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 35.3\" width=\"503\" height=\"308\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-35.3.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-35.3-300x184.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Solve the equation. Determine whether the equation has one solution, no solution, or infinitely many solutions.<\/strong><br \/>\nQuestion 36.<br \/>\n5d &#8211; 8 = 1 + 5d<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n9 + 4t = 12 &#8211; 4t<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 37\" width=\"430\" height=\"336\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-37.png 430w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-37-300x234.png 300w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><\/p>\n<p>Question 38.<br \/>\n3n + 2 = 2(n &#8211; 3)<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n-3(4 &#8211; 2v) = 6v &#8211; 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 39\" width=\"579\" height=\"229\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-39.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-39-300x119.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p><strong>Write an equation of the line that passes through the given point and is parallel to the given line.<\/strong><br \/>\nQuestion 40.<br \/>\n(4, -1); y = -2x + 7<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n(0, 6); y = 5x &#8211; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.3 Question 41\" width=\"579\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-41.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.3-Question-41-300x99.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 42.<br \/>\n(-5, -2); y = \\(\\frac{2}{3}\\)x + 1<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.4_Solving_Special_Systems_of_Linear_Equations\"><\/a>Lesson 5.4 Solving Special Systems of Linear Equations<\/h3>\n<p><strong>Essential Question<\/strong> Can a system of linear equations have no solution or infinitely many solutions?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using a Table to Solve a System<br \/>\nWork with a partner. You invest $450 for equipment to make skateboards. The materials for each skateboard cost $20. You sell each skateboard for $20.<br \/>\na. Write the cost and revenue equations. Then copy and complete the table for your cost C and your revenue R.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.4 1\" width=\"570\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-1.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-1-300x50.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><br \/>\nb. When will your company break even? What is wrong?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36944\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.4 2\" width=\"209\" height=\"148\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Writing and Analyzing a System<br \/>\nWork with a partner. A necklace and matching bracelet have two types of beads. The necklace has 40 small beads and 6 large beads and weighs 10 grams. The bracelet has 20 small beads and 3 large beads and weighs 5 grams. The threads holding the beads have no significant weight.<br \/>\na. Write a system of linear equations that represents the situation. Let x be the weight (in grams) of a small bead and let y be the weight (in grams) of a large bead.<br \/>\nb. Graph the system in the coordinate plane shown. What do you notice about the two lines?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36945\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.4 3\" width=\"206\" height=\"179\" \/><br \/>\nc. Can you find the weight of each type of bead? Explain your reasoning.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nCan a system of linear equations have no solution or infinitely many solutions? Give examples to support your answers.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nDoes the system of linear equations represented by each graph have no solution, one solution, or infinitely many solutions? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-4.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.4 4\" width=\"515\" height=\"155\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-4.png 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-4-300x90.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the system of linear equations.<\/strong><br \/>\nQuestion 1.<br \/>\nx + y = 3<br \/>\n2x + 2y = 6<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ny = -x + 3<br \/>\n2x + 2y = 4<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nx + y = 3<br \/>\nx + 2y = 4<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\ny = -10x + 2<br \/>\n10x + y = 10<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nWhat happens to the solution in Example 3 when the perimeter of the trapezoidal piece of land is 96 kilometers? Explain.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Special_Systems_of_Linear_Equations_5.4_Exercises\"><\/a>Solving Special Systems of Linear Equations 5.4 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>REASONING<\/strong><br \/>\nIs it possible for a system of linear equations to have exactly two solutions? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 1\" width=\"570\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-1.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-1-300x32.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare the graph of a system of linear equations that has infinitely many solutions and the graph of a system of linear equations that has no solution.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u22128, match the system of linear equations with its graph. Then determine whether the system has one solution, no solution, or infinitely many solutions.<\/strong><br \/>\nQuestion 3.<br \/>\n-x + y = 1<br \/>\nx &#8211; y = 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-2.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 2.1\" width=\"361\" height=\"521\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-2.1.png 361w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-2.1-208x300.png 208w\" sizes=\"(max-width: 361px) 100vw, 361px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-2.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 2.2\" width=\"590\" height=\"182\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-2.2.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-2.2-300x93.png 300w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 4.<br \/>\n2x &#8211; 2y = 4<br \/>\n-x + y = -2<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n2x + y = 4<br \/>\n-4x &#8211; 2y = -8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-3.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 3.1\" width=\"430\" height=\"567\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-3.1.png 430w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-3.1-228x300.png 228w\" sizes=\"(max-width: 430px) 100vw, 430px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-3.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 3.2\" width=\"579\" height=\"142\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-3.2.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-3.2-300x74.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 6.<br \/>\nx &#8211; y = 0<br \/>\n5x &#8211; 2y = 6<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n-2x + 4y = 1<br \/>\n3x &#8211; 6y = 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-7.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 7.1\" width=\"592\" height=\"474\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-7.1.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-7.1-300x240.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 8.<br \/>\n5x + 3y = 17<br \/>\nx &#8211; 3y = -2<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36947\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-5.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.4 5\" width=\"343\" height=\"397\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-5.png 343w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-5-259x300.png 259w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/p>\n<p><strong>In Exercises 9\u201316, solve the system of linear equations.<\/strong><br \/>\nQuestion 9.<br \/>\ny = -2x &#8211; 4<br \/>\ny = 2x &#8211; 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 9\" width=\"515\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-9.png 515w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-9-300x288.png 300w\" sizes=\"(max-width: 515px) 100vw, 515px\" \/><\/p>\n<p>Question 10.<br \/>\ny = -6x &#8211; 8<br \/>\ny = -6x + 8<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n3x &#8211; y = 6<br \/>\n-3x + y = -6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 11\" width=\"570\" height=\"227\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-11.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-11-300x119.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 12.<br \/>\n-x + 2y = 7<br \/>\nx &#8211; 2y = 7<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n4x + 4y = -8<br \/>\n-2x &#8211; 2y = 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 13\" width=\"565\" height=\"228\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-13.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-13-300x121.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 14.<br \/>\n15x &#8211; 5y = -20<br \/>\n-3x + y = 4<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n9x &#8211; 15y = 24<br \/>\n6x &#8211; 10y = -16<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 15\" width=\"550\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-15.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-15-300x132.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 16.<br \/>\n3x &#8211; 2y = -5<br \/>\n4x + 5y = 47<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 17\u201322, use only the slopes and y-intercepts of the graphs of the equations to determine whether the system of linear equations has one solution, no solution, or infinitely many solutions. Explain.<\/strong><br \/>\nQuestion 17.<br \/>\ny = 7x + 13<br \/>\n-21x + 3y = 39<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-17.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 17.1\" width=\"584\" height=\"345\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-17.1.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-17.1-300x177.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 18.<br \/>\ny = -6x &#8211; 2<br \/>\n12x + 2y = -6<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n4x + 3y = 27<br \/>\n4x &#8211; 3y = -27<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 19\" width=\"580\" height=\"412\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-19.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-19-300x213.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 20.<br \/>\n-7x + 7y = 1<br \/>\n2x &#8211; 2y = -18<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n-18x + 6y = 24<br \/>\n3x &#8211; y = -2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 21\" width=\"600\" height=\"350\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-21.png 600w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-21-300x175.png 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>Question 22.<br \/>\n2x &#8211; 2y = 16<br \/>\n3x &#8211; 6y = 30<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 23 and 24, describe and correct the error in solving the system of linear equations.<br \/>\nQuestion 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36948\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-6.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.4 6\" width=\"324\" height=\"193\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-6.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-6-300x179.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-23.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 23.1\" width=\"585\" height=\"491\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-23.1.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-23.1-300x252.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-23.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 23.2\" width=\"531\" height=\"234\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-23.2.png 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-23.2-300x132.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-7.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.4 7\" width=\"319\" height=\"111\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-7.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-7-300x104.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA small bag of trail mix contains 3 cups of dried fruit and 4 cups of almonds. A large bag contains 4\\(\\frac{1}{2}\\) cups of dried fruit and 6 cups of almonds. Write and solve a system of linear equations to find the price of 1 cup of dried fruit and 1 cup of almonds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36950\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-8.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.4 8\" width=\"269\" height=\"178\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-25.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 25.1\" width=\"597\" height=\"510\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-25.1.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-25.1-300x256.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nIn a canoe race, Team A is traveling 6 miles per hour and is 2 miles ahead of Team B. Team B is also traveling 6 miles per hour. The teams continue traveling at their current rates for the remainder of the race. Write a system of linear equations that represents this situation. Will Team B catch up to Team A? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA train travels from New York City to Washington, D.C., and then back to New York City. The table shows the number of tickets purchased for each leg of the trip. The cost per ticket is the same for each leg of the trip. Is there enough information to determine the cost of one coach ticket? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36951\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-9.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.4 9\" width=\"330\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-9.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-9-300x105.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-27.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 27.1\" width=\"588\" height=\"577\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-27.1.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-27.1-300x294.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-27.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 27.2\" width=\"552\" height=\"433\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-27.2.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-27.2-300x235.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nWrite a system of three linear equations in two variables so that any two of the equations have exactly one solution, but the entire system of equations has no solution.<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>REASONING<\/strong><br \/>\nIn a system of linear equations, one equation has a slope of 2 and the other equation has a slope of &#8211;\\(\\frac{1}{3}\\). How many solutions does the system have? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 29\" width=\"577\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-29.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-29-300x60.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph shows information about the last leg of a 4 \u00d7 200-meter relay for three relay teams. Team A\u2019s runner ran about 7.8 meters per second, Team B\u2019s runner ran about 7.8 meters per second, and Team C\u2019s runner ran about 8.8 meters per second.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-10.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.4 10\" width=\"288\" height=\"197\" \/><br \/>\na. Estimate the distance at which Team C\u2019s runner passed Team B\u2019s runner.<br \/>\nb. If the race was longer, could Team C\u2019s runner have passed Team A\u2019s runner? Explain.<br \/>\nc. If the race was longer, could Team B\u2019s runner have passed Team A\u2019s runner? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nConsider the system of linear equations y = ax + 4 and y = bx &#8211; 2, where a and b are real numbers. Determine whether each statement is always, sometimes, or never true. Explain your reasoning.<br \/>\na. The system has infinitely many solutions.<br \/>\nb. The system has no solution.c. When a &lt; b, the system has one solution.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 31\" width=\"600\" height=\"318\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-31.png 600w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-31-300x159.png 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nOne admission to an ice skating rink costs x dollars, and renting a pair of ice skates costs y dollars. Your friend says she can determine the exact cost of one admission and one skate rental. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-11.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.4 11\" width=\"316\" height=\"121\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-11.png 316w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-11-300x115.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Solve the equation. Check your solutions.<\/strong><br \/>\nQuestion 33.<br \/>\n|2x + 6| = |x|<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 33\" width=\"563\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-33.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-33-300x279.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 34.<br \/>\n|3x &#8211; 45| = |12x|<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n|x &#8211; 7| = |2x &#8211; 8|<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-35.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 35.1\" width=\"504\" height=\"357\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-35.1.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-35.1-300x213.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-35.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.4 Question 35.2\" width=\"541\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-35.2.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-Question-35.2-300x144.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 36.<br \/>\n|2x + 1| = |3x &#8211; 11|<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_Study_Skills:_Analyzing_Your_Errors\"><\/a>Solving Systems of Linear Equations Study Skills: Analyzing Your Errors<\/h3>\n<p><strong>5.1 &#8211; 5.4 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\nsystem of linear equations, p. 236<br \/>\nsolution of a system of linear equations, p. 236<\/p>\n<p><strong>Core Concepts<\/strong><br \/>\nSection 5.1<br \/>\nSolving a System of Linear Equations by Graphing, p. 237<\/p>\n<p>Section 5.2<br \/>\nSolving a System of Linear Equations by Substitution, p. 242<\/p>\n<p>Section 5.3<br \/>\nSolving a System of Linear Equations by Elimination, p. 248<\/p>\n<p>Section 5.4<br \/>\nSolutions of Systems of Linear Equations, p. 254<\/p>\n<p><strong>Mathematical Practices<\/strong><\/p>\n<p>Question 1.<br \/>\nDescribe the given information in Exercise 33 on page 246 and your plan for finding the solution.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nDescribe another real-life situation similar to Exercise 22 on page 251 and the mathematics that you can apply to solve the problem.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nWhat question(s) can you ask your friend to help her understand the error in the statement she made in Exercise 32 on page 258?<br \/>\nAnswer:<\/p>\n<p><strong>Study Skills: Analyzing Your Errors<\/strong><\/p>\n<p><strong>Study Errors<\/strong><br \/>\nWhat Happens: You do not study the right material or you do not learn it well enough to remember it on a test without resources such as notes.<br \/>\nHow to Avoid This Error: Take a practice test. Work with a study group. Discuss the topics on the test with your teacher. Do not try to learn a whole chapter\u2019s worth of material in one night.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-12.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.4 12\" width=\"363\" height=\"266\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-12.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.4-12-300x220.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_5.1\u20135.4_Quiz\"><\/a>Solving Systems of Linear Equations 5.1\u20135.4 Quiz<\/h3>\n<p><strong>Use the graph to solve the system of linear equations. Check your solution.<\/strong><br \/>\nQuestion 1.<br \/>\ny = &#8211; \\(\\frac{1}{3}\\)x + 2<br \/>\ny = x &#8211; 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36955\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-q-1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations q 1\" width=\"156\" height=\"161\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 1<br \/>\ny = 4x + 6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36956\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-q-2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations q 2\" width=\"162\" height=\"155\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ny = 1<br \/>\ny = 2x + 1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-q-3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations q 3\" width=\"166\" height=\"161\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Solve the system of linear equations by substitution. Check your solution.<\/strong><br \/>\nQuestion 4.<br \/>\ny = x &#8211; 4<br \/>\n-2x + y = 18<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n2y + x = -4<br \/>\ny &#8211; x = -5<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n3x &#8211; 5y = 13<br \/>\nx + 4y = 10<br \/>\nAnswer:<\/p>\n<p>Solve the system of linear equations by elimination. Check your solution.<br \/>\nQuestion 7.<br \/>\nx + y = 4<br \/>\n-3x &#8211; y = -8<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nx + 3y = 1<br \/>\n5x + 6y = 14<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n2x &#8211; 3y = -5<br \/>\n5x + 2y = 16<br \/>\nAnswer:<\/p>\n<p><strong>Solve the system of linear equations.<\/strong><br \/>\nQuestion 10.<br \/>\nx &#8211; y = 1<br \/>\nx &#8211; y = 6<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n6x + 2y = 16<br \/>\n2x &#8211; y = 2<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n3x &#8211; 3y = -2<br \/>\n-6x + 6y = 4<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nYou plant a spruce tree that grows 4 inches per year and a hemlock tree that grows 6 inches per year. The initial heights are shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36958\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-q-4.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations q 4\" width=\"232\" height=\"205\" \/><br \/>\na. Write a system of linear equations that represents this situation.<br \/>\nb. Solve the system by graphing. Interpret your solution.<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nIt takes you 3 hours to drive to a concert 135 miles away. You drive 55 miles per hour on highways and 40 miles per hour on the rest of the roads.<br \/>\na. How much time do you spend driving at each speed?<br \/>\nb. How many miles do you drive on highways? the rest of the roads?<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nIn a football game, all of the home team\u2019s points are from 7-point touchdowns and 3-point field goals. The team scores six times. Write and solve a system of linear equations to find the numbers of touchdowns and field goals that the home team scores.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36959\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-q-5.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 5 Solving Systems of Linear Equations q 5\" width=\"285\" height=\"139\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_5.5_Solving_Equations_by_Graphing\"><\/a>Lesson 5.5 Solving Equations by Graphing<\/h3>\n<p><strong>Essential Question<\/strong> How can you use a system of linear equations to solve an equation with variables on both sides?<\/p>\n<p>Previously, you learned how to use algebra to solve equations with variables on both sides. Another way is to use a system of linear equations.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Solving an Equation by Graphing<br \/>\nWork with a partner. Solve 2x &#8211; 1 = &#8211; \\(\\frac{1}{2}\\) x + 4 by graphing.<br \/>\na. Use the left side to write a linear equation. Then use the right side to write another linear equation.<br \/>\nb. Graph the two linear equations from part (a). Find the x-value of the point of intersection. Check that the x-value is the solution of<br \/>\n2x &#8211; 1 = &#8211;\\(\\frac{1}{2}\\)x + 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36960\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.5 1\" width=\"439\" height=\"199\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-1.png 439w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-1-300x136.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><br \/>\nc. Explain why this \u201cgraphical method\u201d works.<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Solving Equations Algebraically and Graphically<br \/>\nWork with a partner. Solve each equation using two methods.<br \/>\nMethod 1 Use an algebraic method.<br \/>\nMethod 2 Use a graphical method.<br \/>\nIs the solution the same using both methods?<br \/>\na. \\(\\frac{1}{2}\\)x + 4 = &#8211;\\(\\frac{1}{4}\\)x + 1<br \/>\nb. \\(\\frac{2}{3}\\)x + 4 = \\(\\frac{1}{3}\\)x + 3<br \/>\nc. &#8211;\\(\\frac{2}{3}\\) x &#8211; 1 = \\(\\frac{1}{3}\\)x &#8211; 4<br \/>\nd. \\(\\frac{4}{5}\\) x + \\(\\frac{7}{5}\\) = 3x &#8211; 3<br \/>\ne. -x + 2.5 = 2x &#8211; 0.5<br \/>\nf. &#8211; 3x + 1.5 = x + 1.5<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you use a system of linear equations to solve an equation with variables on both sides?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nCompare the algebraic method and the graphical method for solving a linear equation with variables on both sides. Describe the advantages and disadvantages of each method.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the equation by graphing. Check your solution.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\frac{1}{2}\\)x &#8211; 3 = 2x<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n-4 + 9x = -3x + 2<br \/>\nAnswer:<\/p>\n<p>Solve the equation by graphing. Check your solutions.<br \/>\nQuestion 3.<br \/>\n|2x + 2| = |x &#8211; 2|<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n|x &#8211; 6| = |-x + 4|<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nCompany C charges $3.30 per mile plus a flat fee of $115 per week. After how many miles are the total costs the same at Company A and Company C?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Equations_by_Graphing_5.5_Exercises\"><\/a>Solving Equations by Graphing 5.5 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe graphs of the equations y = 3x &#8211; 20 and y = -2x + 10 intersect at the point (6, \u22122). Without solving, find the solution of the equation 3x &#8211; 20 = -2x + 10.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 1\" width=\"348\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-1.png 348w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-1-300x32.png 300w\" sizes=\"(max-width: 348px) 100vw, 348px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to rewrite the absolute value equation |2x &#8211; 4| = |-5x + 1| as two systems of linear equations.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20136, use the graph to solve the equation. Check your solution.<\/strong><br \/>\nQuestion 3.<br \/>\n-2x + 3 = x<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36961\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.5 2\" width=\"134\" height=\"129\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 3\" width=\"527\" height=\"264\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-3.png 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-3-300x150.png 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><\/p>\n<p>Question 4.<br \/>\n-3 = 4x + 1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36962\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-3.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.5 3\" width=\"137\" height=\"131\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n-x &#8211; 1 = \\(\\frac{1}{3}\\)x + 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36963\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-4.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.5 4\" width=\"138\" height=\"136\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 5\" width=\"504\" height=\"319\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-5.png 504w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-5-300x190.png 300w\" sizes=\"(max-width: 504px) 100vw, 504px\" \/><\/p>\n<p>Question 6.<br \/>\n&#8211;\\(\\frac{3}{2}\\)x &#8211; 2 = -4x + 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36964\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-5.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.5 5\" width=\"142\" height=\"132\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 7\u221214, solve the equation by graphing. Check your solution.<\/strong><br \/>\nQuestion 7.<br \/>\nx + 4 = -x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 7\" width=\"549\" height=\"465\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-7.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-7-300x254.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 8.<br \/>\n4x = x + 3<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nx + 5 = -2x &#8211; 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 9\" width=\"566\" height=\"504\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-9.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-9-300x267.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 10.<br \/>\n-2x + 6 = 5x &#8211; 1<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{1}{2}\\)x &#8211; 2 = 9 &#8211; 5x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 11\" width=\"554\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-11.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-11-300x283.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 12.<br \/>\n-5 + \\(\\frac{1}{4}\\)x = 3x + 6<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n5x &#8211; 7 = 2(x + 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 13\" width=\"556\" height=\"568\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-13.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-13-294x300.png 294w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 14.<br \/>\n-6(x + 4) = -3x &#8211; 6<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 15\u221220, solve the equation by graphing. Determine whether the equation has one solution, no solution, or infinitely many solutions.<\/strong><br \/>\nQuestion 15.<br \/>\n3x &#8211; 1 = -x + 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 15\" width=\"544\" height=\"503\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-15.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-15-300x277.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 16.<br \/>\n5x &#8211; 4 = 5x + 1<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n-4(2 &#8211; x) = 4x &#8211; 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 17\" width=\"554\" height=\"428\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-17.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-17-300x232.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 18.<br \/>\n-2x &#8211; 3 = 2(x &#8211; 2)<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n-x &#8211; 5 = &#8211;\\(\\frac{1}{3}\\) (3x + 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 19\" width=\"549\" height=\"488\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-19.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-19-300x267.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\frac{1}{2}\\)(8x + 3) = 4x + \\(\\frac{3}{2}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 21 and 22, use the graphs to solve the equation. Check your solutions.<\/strong><br \/>\nQuestion 21.<br \/>\n|x &#8211; 4| = |3x|<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36965\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-6.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.5 6\" width=\"306\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-6.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-6-300x129.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 21\" width=\"547\" height=\"265\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-21.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-21-300x145.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 22.<br \/>\n|2x + 4| = |x &#8211; 1|<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36966\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-7.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.5 7\" width=\"309\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-7.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-7-300x120.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 23\u221230, solve the equation by graphing. Check your solutions.<\/strong><br \/>\nQuestion 23.<br \/>\n|2x| = |x + 3|<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-23.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 23.1\" width=\"509\" height=\"505\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-23.1.png 509w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-23.1-300x298.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-23.1-150x150.png 150w\" sizes=\"(max-width: 509px) 100vw, 509px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-23.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 23.2\" width=\"550\" height=\"262\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-23.2.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-23.2-300x143.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 24.<br \/>\n|2x &#8211; 6| = |x|<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n|-x + 4| = |2x &#8211; 2|<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-25.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 25.1\" width=\"510\" height=\"500\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-25.1.png 510w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-25.1-300x294.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-25.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 25.2\" width=\"575\" height=\"343\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-25.2.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-25.2-300x179.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 26.<br \/>\n|x + 2| = |-3x + 6|<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n|x + 1| = |x &#8211; 5|<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-27.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 27.1\" width=\"510\" height=\"505\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-27.1.png 510w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-27.1-300x297.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-27.1-150x150.png 150w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-27.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 27.2\" width=\"526\" height=\"294\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-27.2.png 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-27.2-300x168.png 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p>Question 28.<br \/>\n|2x + 5| = |-2x + 1|<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n|x &#8211; 3| = 2|x|<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-29.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 29.1\" width=\"558\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-29.1.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-29.1-300x266.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-29.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 29.2\" width=\"540\" height=\"266\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-29.2.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-29.2-300x148.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 30.<br \/>\n4|x + 2| = |2x + 7|<br \/>\nAnswer:<\/p>\n<p><strong>USING TOOLS<\/strong> In Exercises 31 and 32, use a graphing calculator to solve the equation.<br \/>\nQuestion 31.<br \/>\n0.7x + 0.5 = -0.2x &#8211; 1.3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 31\" width=\"526\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-31.png 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-31-300x106.png 300w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><\/p>\n<p>Question 32.<br \/>\n2.1x + 0.6 = -1.4x + 6.9<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou need to hire a catering company to serve meals to guests at a wedding reception. Company A charges $500 plus $20 per guest. Company B charges $800 plus $16 per guest. For how many guests are the total costs the same at both companies?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 33\" width=\"574\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-33.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-33-300x273.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYour dog is 16 years old in dog years. Your cat is 28 years old in cat years. For every human year, your dog ages by 7 dog years and your cat ages by 4 cat years. In how many human years will both pets be the same age in their respective types of years?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36967\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-8.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.5 8\" width=\"263\" height=\"160\" \/><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou and a friend race across a field to a fence and back. Your friend has a 50-meter head start. The equations shown represent you and your friend\u2019s distances d (in meters) from the fence t seconds after the race begins. Find the time at which you catch up to your friend.<br \/>\nYou: d = |-5t + 100|<br \/>\nYour friend: d = |-3\\(\\frac{1}{3}\\)t + 50|<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 35\" width=\"567\" height=\"434\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-35.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-35-300x230.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nThe graphs of y = -x + 4 and y = 2x &#8211; 8 intersect at the point (4, 0). So, your friend says the solution of the equation -x + 4 = 2x &#8211; 8 is (4, 0). Is your friend correct? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nFind values for m and b so that the solution of the equation mx + b = &#8211; 2x &#8211; 1 is x = -3.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 37\" width=\"567\" height=\"339\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-37.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-37-300x179.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph shows the total revenue and expenses of a company x years after it opens for business.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36968\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-9.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.5 9\" width=\"240\" height=\"195\" \/><br \/>\na. Estimate the point of intersection of the graphs.<br \/>\nb. Interpret your answer in part (a).<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe value of the perimeter of the triangle (in feet) is equal to the value of the area of the triangle (in square feet). Use a graph to find x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36969\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-10.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 5 Solving Systems of Linear Equations 5.5 10\" width=\"174\" height=\"118\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 39\" width=\"540\" height=\"315\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-39.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-39-300x175.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nA car has an initial value of $20,000 and decreases in value at a rate of $1500 per year. Describe a different car that will be worth the same amount as this car in exactly 5 years. Specify the initial value and the rate at which the value decreases.<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nUse a graph to determine the sign of the solution of the equation ax + b = cx + d in each situation.<br \/>\na. 0 &lt; b &lt; d and a &lt; c<br \/>\nb. d &lt; b &lt; 0 and a &lt; c Answer: Maintaining Mathematical Proficiency Graph the inequality.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-41.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 41.1\" width=\"591\" height=\"450\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-41.1.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-41.1-300x228.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-41.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 41.2\" width=\"286\" height=\"243\" \/><\/p>\n<p>Question 42.<br \/>\ny &gt; 5<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\nx \u2264 -2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 43\" width=\"327\" height=\"44\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-43.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-43-300x40.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><\/p>\n<p>Question 44.<br \/>\nn \u2265 9<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\nc &lt; -6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 45\" width=\"319\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-45.png 319w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-45-300x64.png 300w\" sizes=\"(max-width: 319px) 100vw, 319px\" \/><\/p>\n<p><strong>Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.<\/strong><br \/>\nQuestion 46.<br \/>\nf(x) = x &#8211; 5; g(x) = f(x + 2)<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\nf(x) = 6x; g(x) = -f(x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 47\" width=\"582\" height=\"455\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-47.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-47-300x235.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 48.<br \/>\nf(x) = -2x + 1; g(x) = f(4x)<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\nf(x) = \\(\\frac{1}{2}\\)x &#8211; 2; g(x) = f(x &#8211; 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.5 Question 49\" width=\"569\" height=\"484\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-49.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.5-Question-49-300x255.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<h3><a id=\"Lesson_5.6_Graphing_Linear_Inequalities_in_Two_Variables\"><\/a>Lesson 5.6 Graphing Linear Inequalities in Two Variables<\/h3>\n<p><strong>Essential Question<\/strong> How can you graph a linear inequality in two variables?<br \/>\nA solution of a linear inequality in two variables is an ordered pair (x, y) that makes the inequality true. The graph of a linear inequality in two variables shows all the solutions of the inequality in a coordinate plane.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Writing a Linear Inequality in Two Variables<br \/>\nWork with a partner.<br \/>\na. Write an equation represented by the dashed line.<br \/>\nb. The solutions of an inequality are represented by the shaded region. In words, describe the solutions of the inequality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36970\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 1\" width=\"203\" height=\"197\" \/><br \/>\nc. Write an inequality represented by the graph. Which inequality symbol did you use? Explain your reasoning.<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Using a Graphing Calculator<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36971\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 2\" width=\"219\" height=\"183\" \/><br \/>\nWork with a partner. Use a graphing calculator to graph y \u2265 \\(\\frac{1}{4}\\)x &#8211; 3.<br \/>\na. Enter the equation y = \\(\\frac{1}{4}\\)x &#8211; 3 into your calculator.<br \/>\nb. The inequality has the symbol \u2265. So, the region to be shaded is above the graph of y = \\(\\frac{1}{4}\\)x &#8211; 3, as shown. Verify this by testing a point in this region, such as (0, 0), to make sure it is a solution of the inequality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36972\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 3\" width=\"236\" height=\"158\" \/><br \/>\nBecause the inequality symbol is greater than or equal to, the line is solid and not dashed. Some graphing calculators always use a solid line when graphing inequalities. In this case, you have to determine whether the line should be solid or dashed, based on the inequality symbol used in the original inequality<\/p>\n<p><strong>EXPLORATION 3<\/strong><\/p>\n<p>Graphing Linear Inequalities in Two Variables<br \/>\nWork with a partner. Graph each linear inequality in two variables. Explain your steps. Use a graphing calculator to check your graphs.<br \/>\na. y &gt; x + 5<br \/>\nb. y \u2264 &#8211;\\(\\frac{1}{2}\\)x + 1<br \/>\nc. y \u2265 -x &#8211; 5<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 4.<br \/>\nHow can you graph a linear inequality in two variables?<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nGive an example of a real-life situation that can be modeled using a linear inequality in two variables.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Tell whether the ordered pair is a solution of the inequality.<\/strong><br \/>\nQuestion 1.<br \/>\nx + y &gt; 0; (-2, 2)<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n4x &#8211; y \u2265 5; (0, 0)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n5x &#8211; 2y \u2264 -1; (-4, -1)<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n-2x &#8211; 3y &lt; 15; (5, -7)<br \/>\nAnswer:<\/p>\n<p><strong>Graph the inequality in a coordinate plane.<\/strong><br \/>\nQuestion 5.<br \/>\ny &gt; -1<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nx \u2264 -4<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nx + y \u2264 -4<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nx &#8211; 2y &lt; 0<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nYou can spend at most $12 on red peppers and tomatoes for salsa. Red peppers cost $4 per pound, and tomatoes cost $3 per pound. Write and graph an inequality that represents the amounts of red peppers and tomatoes you can buy. Identify and interpret two solutions of the inequality.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_Linear_Inequalities_in_Two_Variables_5.6_Exercises\"><\/a>Graphing Linear Inequalities in Two Variables 5.6 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nHow can you tell whether an ordered pair is a solution of a linear inequality?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 1\" width=\"557\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-1.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-1-300x91.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare the graph of a linear inequality in two variables with the graph of a linear equation in two variables.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u201310, tell whether the ordered pair is a solution of the inequality.<\/strong><br \/>\nQuestion 3.<br \/>\nx + y &lt; 7; (2, 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 3\" width=\"368\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-3.png 368w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-3-300x117.png 300w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><\/p>\n<p>Question 4.<br \/>\nx &#8211; y \u2264 0; (5, 2)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nx + 3y \u2265 -2; (-9, 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 5\" width=\"421\" height=\"183\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-5.png 421w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-5-300x130.png 300w\" sizes=\"(max-width: 421px) 100vw, 421px\" \/><\/p>\n<p>Question 6.<br \/>\n8x + y &gt; -6; (-1, 2)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n-6x + 4y \u2264 6; (-3, -3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 7\" width=\"412\" height=\"189\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-7.png 412w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-7-300x138.png 300w\" sizes=\"(max-width: 412px) 100vw, 412px\" \/><\/p>\n<p>Question 8.<br \/>\n3x &#8211; 5y \u2265 2; (-1, -1)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n-x &#8211; 6y &gt; 12; (-8, 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 9\" width=\"424\" height=\"183\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-9.png 424w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-9-300x129.png 300w\" sizes=\"(max-width: 424px) 100vw, 424px\" \/><\/p>\n<p>Question 10.<br \/>\n-4x &#8211; 8y &lt; 15; (-6, 3)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 11\u221216, tell whether the ordered pair is a solution of the inequality whose graph is shown.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-4.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 4\" width=\"136\" height=\"129\" \/><br \/>\nQuestion 11.<br \/>\n(0, -1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 11\" width=\"549\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-11.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-11-300x33.png 300w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 12.<br \/>\n(-1, 3)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n(1, 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 13\" width=\"566\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-13.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-13-300x20.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 14.<br \/>\n(0, 0)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n(3, 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 15\" width=\"547\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-15.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-15-300x20.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 16.<br \/>\n(2, 1)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA carpenter has at most $250 to spend on lumber. The inequality 8x + 12y \u2264 250 represents the numbers x of 2-by-8boards and the numbers y of 4-by-4 boards the carpenter can buy. Can the carpenter buy twelve 2-by-8 boards and fourteen 4-by-4 boards? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36974\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 5\" width=\"290\" height=\"111\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 17\" width=\"569\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-17.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-17-300x131.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 18.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe inequality 3x + 2y \u2265 93 represents the numbers x of multiple- choice questions and the numbers y of matching questions you can answer correctly to receive an A on a test. You answer 20 multiple-choice questions and 18 matching questions correctly. Do you receive an A on the test? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 19\u201324, graph the inequality in a coordinate plane.<\/strong><br \/>\nQuestion 19.<br \/>\ny \u2264 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 19\" width=\"373\" height=\"238\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-19.png 373w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-19-300x191.png 300w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><\/p>\n<p>Question 20.<br \/>\ny &gt; 6<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nx &lt; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 21\" width=\"375\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-21.png 375w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-21-300x194.png 300w\" sizes=\"(max-width: 375px) 100vw, 375px\" \/><\/p>\n<p>Question 22.<br \/>\nx \u2265 -3<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\ny &gt; -7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 23\" width=\"402\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-23.png 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-23-300x177.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p>Question 24.<br \/>\nx &lt; 9<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 25\u221230, graph the inequality in a coordinate plane.<\/strong><br \/>\nQuestion 25.<br \/>\ny &gt; -2x &#8211; 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 25\" width=\"447\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-25.png 447w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-25-300x160.png 300w\" sizes=\"(max-width: 447px) 100vw, 447px\" \/><\/p>\n<p>Question 26.<br \/>\ny \u2264 3x &#8211; 1<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n-4x + y &lt; -7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 27\" width=\"496\" height=\"343\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-27.png 496w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-27-300x207.png 300w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><\/p>\n<p>Question 28.<br \/>\n3x &#8211; y \u2265 5<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n5x &#8211; 2y \u2264 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 29\" width=\"476\" height=\"450\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-29.png 476w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-29-300x284.png 300w\" sizes=\"(max-width: 476px) 100vw, 476px\" \/><\/p>\n<p>Question 30.<br \/>\n-x + 4y &gt; -12<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 31 and 32, describe and correct the error in graphing the inequality.<br \/>\nQuestion 31.<br \/>\ny &lt; -x + 1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-6.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 6\" width=\"277\" height=\"142\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 31\" width=\"308\" height=\"256\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-31.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-31-300x249.png 300w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><\/p>\n<p>Question 32.<br \/>\ny \u2264 3x &#8211; 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36976\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 7\" width=\"273\" height=\"145\" \/><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou have at most $20 to spend at an arcade. Arcade games cost $0.75 each, and snacks cost $2.25 each. Write and graph an inequality that represents the numbers of games you can play and snacks you can buy. Identify and interpret two solutions of the inequality.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-33.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 33.1\" width=\"575\" height=\"456\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-33.1.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-33.1-300x238.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44934\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-33.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 33.2\" width=\"337\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-33.2.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-33.2-215x300.png 215w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44935\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-33.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 33.3\" width=\"627\" height=\"331\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-33.3.png 627w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-33.3-300x158.png 300w\" sizes=\"(max-width: 627px) 100vw, 627px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA drama club must sell at least $1500 worth of tickets to cover the expenses of producing a play. Write and graph an inequality that represents how many adult and student tickets the club must sell. Identify and interpret two solutions of the inequality.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36977\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-8.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 8\" width=\"177\" height=\"119\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 35\u201338, write an inequality that represents the graph.<\/strong><br \/>\nQuestion 35.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36978\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 9\" width=\"130\" height=\"124\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 35\" width=\"547\" height=\"429\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-35.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-35-300x235.png 300w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 36.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36979\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-10.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 10\" width=\"141\" height=\"124\" \/><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36980\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 11\" width=\"133\" height=\"126\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 37\" width=\"588\" height=\"453\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-37.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-37-300x231.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36981\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-12.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 12\" width=\"131\" height=\"122\" \/><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nLarge boxes weigh 75 pounds, and small boxes weigh 40 pounds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36982\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 13\" width=\"173\" height=\"224\" \/><br \/>\na. Write and graph an inequality that represents the numbers of large and small boxes a 200-pound delivery person can take on the elevator.<br \/>\nb. Explain why some solutions of the inequality might not be practical in real life.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-39.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 39.1\" width=\"588\" height=\"558\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-39.1.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-39.1-300x285.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-39.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 39.2\" width=\"347\" height=\"474\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-39.2.png 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-39.2-220x300.png 220w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44940\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-39.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 39.3\" width=\"578\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-39.3.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-39.3-300x88.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nMatch each inequality with its graph.<br \/>\na. 3x &#8211; 2y \u2264 6<br \/>\nb. 3x &#8211; 2y &lt; 6 c. 3x &#8211; 2y &gt; 6<br \/>\nd. 3x &#8211; 2y \u2265 6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36983\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-14.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 5 Solving Systems of Linear Equations 5.6 14\" width=\"316\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-14.png 316w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-14-300x247.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhen graphing a linear inequality in two variables, why must you choose a test point that is not on the boundary line?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 41\" width=\"578\" height=\"119\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-41.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-41-300x62.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nWrite a linear inequality in two variables that has the following two properties.<br \/>\n\u2022 (0, 0), (0, -1), and (0, 1) are not solutions.<br \/>\n\u2022 (1, 1), (3, -1), and (-1, 3) are solutions.<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>WRITING<\/strong><br \/>\nCan you always use (0, 0) as a test point when graphing an inequality? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 43\" width=\"578\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-43.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-43-300x31.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p><strong>CRITICAL THINKING<\/strong><br \/>\nIn Exercises 44 and 45, write and graph an inequality whose graph is described by the given information.<br \/>\nQuestion 44.<br \/>\nThe points (2, 5) and (\u22123, \u22125) lie on the boundary line. The points (6, 5) and (\u22122, \u22123) are solutions of the inequality.<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\nThe points (\u22127, \u221216) and (1, 8) lie on the boundary line. The points (\u22127, 0) and (3, 14) are not solutions of the inequality.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-45.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 45.1\" width=\"567\" height=\"395\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-45.1.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-45.1-300x209.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44944\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-45.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 45.2\" width=\"567\" height=\"230\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-45.2.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-45.2-300x122.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Write the next three terms of the arithmetic sequence.<\/strong><br \/>\nQuestion 46.<br \/>\n0, 8, 16, 24, 32, . . .<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n-5, -8, -11, -14, -17, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44945\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-47.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.6 Question 47.1\" width=\"593\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-47.1.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.6-Question-47.1-300x112.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><\/p>\n<p>Question 48.<br \/>\n\\(-\\frac{3}{2},-\\frac{1}{2}, \\frac{1}{2}, \\frac{3}{2}, \\frac{5}{2}, \\ldots\\)<\/p>\n<h3><a id=\"Lesson_5.7_Systems_of_Linear_Inequalities\"><\/a>Lesson 5.7 Systems of Linear Inequalities<\/h3>\n<p><strong>Essential Question <\/strong>How can you graph a system of linear inequalities?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Graphing Linear Inequalities<br \/>\nWork with a partner. Match each linear inequality with its graph. Explain your reasoning.<br \/>\n2x + y \u2264 4 Inequality 1<br \/>\n2x &#8211; y \u2264 0 Inequality 2<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36984\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 1\" width=\"478\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-1.png 478w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-1-300x116.png 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Graphing a System of Linear Inequalities<br \/>\nWork with a partner. Consider the linear inequalities given in Exploration 1.<br \/>\n2x + y \u2264 4 Inequality 1<br \/>\n2x &#8211; y \u2264 0 Inequality 2<br \/>\na. Use two different colors to graph the inequalities in the same coordinate plane. What is the result?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 2\" width=\"227\" height=\"152\" \/><br \/>\nb. Describe each of the shaded regions of the graph. What does the unshaded region represent?<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36986\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 3\" width=\"196\" height=\"185\" \/><br \/>\nQuestion 3.<br \/>\nHow can you graph a system of linear inequalities?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nWhen graphing a system of linear inequalities, which region represents the solution of the system?<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nDo you think all systems of linear inequalities have a solution? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nWrite a system of linear inequalities represented by the graph.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Tell whether the ordered pair is a solution of the system of linear inequalities.<\/strong><br \/>\nQuestion 1.<br \/>\n(-1, 5); y &lt; 5 y &gt; x &#8211; 4<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n(1, 4); y \u2265 3x + 1<br \/>\ny &gt; x &#8211; 1<br \/>\nAnswer:<\/p>\n<p><strong>Graph the system of linear inequalities.<\/strong><br \/>\nQuestion 3.<br \/>\ny \u2265 -x + 4<br \/>\nx + y \u2264 0<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\ny &gt; 2x &#8211; 3<br \/>\ny \u2265 \\(\\frac{1}{2}\\)x + 1<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n-2x + y &lt; 4 2x + y &gt; 4<br \/>\nAnswer:<\/p>\n<p><strong>Write a system of linear inequalities represented by the graph.<\/strong><br \/>\nQuestion 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36987\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-4.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 4\" width=\"138\" height=\"133\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 5\" width=\"140\" height=\"132\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nName another solution of Example 6.<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nYou want to spend at least 3 hours at the mall. How does this change the system? Is (2.5, 5) still a solution? Explain.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Systems_of_Linear_Inequalities_5.7_Exercises\"><\/a>Systems of Linear Inequalities 5.7 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><br \/>\nQuestion 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nHow can you verify that an ordered pair is a solution of a system of linear inequalities?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 1\" width=\"548\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-1.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-1-300x33.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nUse the graph shown. Which of the ordered pairs does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-6.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 6\" width=\"543\" height=\"149\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-6.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-6-300x82.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u22126, tell whether the ordered pair is a solution of the system of linear inequalities.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 7\" width=\"133\" height=\"127\" \/><br \/>\nQuestion 3.<br \/>\n(-4, 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44947\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 3\" width=\"586\" height=\"113\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-3.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-3-300x58.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 4.<br \/>\n(-3, -1)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n(-2, 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44948\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 5\" width=\"569\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-5.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-5-300x30.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 6.<br \/>\n(1, 1)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 7\u221210, tell whether the ordered pair is a solution of the system of linear inequalities.<\/strong><br \/>\nQuestion 7.<br \/>\n(-5, 2); y &lt; 4<br \/>\ny &gt; x + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 7\" width=\"488\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-7.png 488w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-7-300x109.png 300w\" sizes=\"(max-width: 488px) 100vw, 488px\" \/><\/p>\n<p>Question 8.<br \/>\n(1, -1); y &gt; -2<br \/>\ny &gt; x &#8211; 5<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n(0, 0); y \u2264 x + 7<br \/>\ny \u2265 2x + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44950\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 9\" width=\"555\" height=\"205\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-9.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-9-300x111.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 10.<br \/>\n(4, -3); y \u2264 -x + 1<br \/>\ny \u2264 5x &#8211; 2<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 11\u221220, graph the system of linear inequalities.<\/strong><br \/>\nQuestion 11.<br \/>\ny &gt; -3<br \/>\ny \u2265 5x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44951\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 11\" width=\"530\" height=\"244\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-11.png 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-11-300x138.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Question 12.<br \/>\ny &lt; -1<br \/>\nx &gt; 4<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\ny &lt; -2 y &gt; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 13\" width=\"536\" height=\"241\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-13.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-13-300x135.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 14.<br \/>\ny &lt; x &#8211; 1<br \/>\ny \u2265 x + 1<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\ny \u2265 -5<br \/>\ny &#8211; 1 &lt; 3x Answer: Question 16. x + y &gt; 4<br \/>\ny \u2265 \\(\\frac{3}{2}\\)x &#8211; 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 15\" width=\"533\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-15.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-15-300x137.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Question 17.<br \/>\nx + y &gt; 1<br \/>\n-x &#8211; y &lt; -3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 17\" width=\"481\" height=\"389\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-17.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-17-300x243.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>Question 18.<br \/>\n2x + y \u2264 5<br \/>\ny + 2 \u2265 -2x<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nx &lt; 4<br \/>\ny &gt; 1<br \/>\ny \u2265 -x + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44955\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 19\" width=\"638\" height=\"298\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-19.png 638w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-19-300x140.png 300w\" sizes=\"(max-width: 638px) 100vw, 638px\" \/><\/p>\n<p>Question 20.<br \/>\nx + y \u2264 10<br \/>\nx &#8211; y \u2265 2<br \/>\ny &gt; 2<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 21\u221226, write a system of linear inequalities represented by the graph.<\/strong><br \/>\nQuestion 21.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-8.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 8\" width=\"130\" height=\"131\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44956\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 21\" width=\"589\" height=\"294\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-21.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-21-300x150.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 22.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 9\" width=\"123\" height=\"133\" \/><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-10.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 10\" width=\"139\" height=\"130\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 23\" width=\"588\" height=\"310\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-23.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-23-300x158.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 11\" width=\"129\" height=\"131\" \/><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-12.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 12\" width=\"131\" height=\"130\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44958\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 25\" width=\"582\" height=\"329\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-25.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-25-300x170.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 13\" width=\"133\" height=\"133\" \/><br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 27 and 28, describe and correct the error in graphing the system of linear inequalities.<br \/>\nQuestion 27.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-14.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 14\" width=\"284\" height=\"159\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44959\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 27\" width=\"572\" height=\"384\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-27.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-27-300x201.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 28.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 15\" width=\"291\" height=\"153\" \/><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou can spend at most $21 on fruit. Blueberries cost $4 per pound, and strawberries cost $3 per pound. You need at least 3 pounds of fruit to make muffins.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-16.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 16\" width=\"203\" height=\"120\" \/><br \/>\na. Write and graph a system of linear inequalities that represents the situation.<br \/>\nb. Identify and interpret a solution of the system.<br \/>\nc. Use the graph to determine whether you can buy 4 pounds of blueberries and 1 pound of strawberries.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44960\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-29.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 29.1\" width=\"567\" height=\"377\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-29.1.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-29.1-300x199.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44961\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-29.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 29.2\" width=\"591\" height=\"578\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-29.2.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-29.2-300x293.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44962\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-29.3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 29.3\" width=\"548\" height=\"127\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-29.3.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-29.3-300x70.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou earn $10 per hour working as a manager at a grocery store. You are required to work at the grocery store at least 8 hours per week. You also teach music lessons for $15 per hour. You need to earn at least $120 per week, but you do not want to work more than 20 hours per week.<br \/>\na. Write and graph a system of linear inequalities that represents the situation.<br \/>\nb. Identify and interpret a solution of the system.<br \/>\nc. Use the graph to determine whether you can work 8 hours at the grocery store and teach 1 hour of music lessons.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are fishing for surfperch and rockfish, which are species of bottomfish. Gaming laws allow you to catch no more than 15 surfperch per day, no more than 10 rockfish per day, and no more than 20 total bottomfish per day.<br \/>\na. Write and graph a system of linear inequalities that represents the situation.<br \/>\nb. Use the graph to determine whether you can catch 11 surfperch and 9 rockfish in 1 day.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 17\" width=\"290\" height=\"134\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44963\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-31.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 31.1\" width=\"574\" height=\"543\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-31.1.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-31.1-300x284.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44964\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-31.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 31.2\" width=\"588\" height=\"396\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-31.2.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-31.2-300x202.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>REASONING<\/strong><br \/>\nDescribe the intersection of the half-planes of the system shown.<br \/>\nx &#8211; y \u2264 4<br \/>\nx &#8211; y \u2265 4<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe following points are the vertices of a shaded rectangle.<br \/>\n(-1, 1), (6, 1), (6, -3), (-1, -3)<br \/>\na. Write a system of linear inequalities represented by the shaded rectangle.<br \/>\nb. Find the area of the rectangle.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44965\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 33\" width=\"567\" height=\"365\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-33.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-33-300x193.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe following points are the vertices of a shaded triangle.<br \/>\n(2, 5), (6, -3), (-2, -3)<br \/>\na. Write a system of linear inequalities represented by the shaded triangle.<br \/>\nb. Find the area of the triangle.<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou plan to spend less than half of your monthly $2000 paycheck on housing and savings. You want to spend at least 10% of your paycheck on savings and at most 30% of it on housing. How much money can you spend on savings and housing?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44966\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-35.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 35.1\" width=\"585\" height=\"332\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-35.1.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-35.1-300x170.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44967\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-35.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 35.2\" width=\"565\" height=\"590\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-35.2.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-35.2-287x300.png 287w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nOn a road trip with a friend, you drive about 70 miles per hour, and your friend drives about 60 miles per hour. The plan is to drive less than 15 hours and at least 600 miles each day. Your friend will drive more hours than you. How many hours can you and your friend each drive in 1 day?<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow are solving systems of linear inequalities and solving systems of linear equations similar? How are they different?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44968\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 37\" width=\"579\" height=\"553\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-37.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-37-300x287.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graphs of two linear equations are shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-18.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 18\" width=\"243\" height=\"157\" \/><br \/>\nReplace the equal signs with inequality symbols to create a system of linear inequalities that has point C as a solution, but not points A, B, and D. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 19\" width=\"120\" height=\"62\" \/><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nWrite a system of linear inequalities that is equivalent to |y| &lt; x, where x &gt; 0. Graph the system.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44969\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 39\" width=\"489\" height=\"365\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-39.png 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-39-300x224.png 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says that a system of linear inequalities in which the boundary lines are parallel must have no solution. Is your friend correct? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIs it possible for the solution set of a system of linear inequalities to be all real numbers? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44970\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 41\" width=\"565\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-41.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-41-300x32.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p><strong>OPEN-ENDED<\/strong> In Exercises 42\u221244, write a system of linear inequalities with the given characteristic.<br \/>\nQuestion 42.<br \/>\nAll solutions are in Quadrant I.<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\nAll solutions have one positive coordinate and one negative coordinate.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44971\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 43\" width=\"516\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-43.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-43-300x49.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<p>Question 44.<br \/>\nThere are no solutions.<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nOne inequality in a system is -4x + 2y &gt; 6. Write another inequality so the system has (a) no solution and (b) infinitely many solutions.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44972\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 45\" width=\"577\" height=\"118\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-45.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-45-300x61.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nYou receive a gift certificate for a clothing store and plan to use it to buy T-shirts and sweatshirts. Describe a situation in which you can buy 9 T-shirts and 1 sweatshirt, but you cannot buy 3 T-shirts and 8 sweatshirts. Write and graph a system of linear inequalities that represents the situation.<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nWrite a system of linear inequalities that has exactly one solution.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44974\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-47.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 47\" width=\"563\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-47.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-47-300x33.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou make necklaces and key chains to sell at a craft fair. The table shows the amounts of time and money it takes to make a necklace and a key chain, and the amounts of time and money you have available for making them.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-20.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 20\" width=\"368\" height=\"123\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-20.png 368w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-20-300x100.png 300w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><br \/>\na. Write and graph a system of four linear inequalities that represents the number x of necklaces and the number y of key chains that you can make.<br \/>\nb. Find the vertices (corner points) of the graph of the system.<br \/>\nc. You sell each necklace for $10 and each key chain for $8. The revenue R is given by the equation R = 10x + 8y. Find the revenue corresponding to each ordered pair in part (b). Which vertex results in the maximum revenue?<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Write the product using exponents.<\/strong><br \/>\nQuestion 49.<br \/>\n4 \u2022 4 \u2022 4 \u2022 4 \u2022 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-49.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 49\" width=\"209\" height=\"27\" \/><\/p>\n<p>Question 50.<br \/>\n(-13) \u2022 (-13) \u2022 (-13)<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\nx \u2022 x \u2022 x \u2022 x \u2022 x \u2022 x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44976\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-51.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 51\" width=\"233\" height=\"30\" \/><\/p>\n<p><strong>Write an equation of the line with the given slope and y-intercept.<\/strong><br \/>\nQuestion 52.<br \/>\nslope: 1<br \/>\ny-intercept: -6<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\nslope: -3<br \/>\ny-intercept: 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44977\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-53.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 53\" width=\"312\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-53.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-53-300x95.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><\/p>\n<p>Question 54.<br \/>\nslope: &#8211;\\(\\frac{1}{4}\\)<br \/>\ny-intercept: -1<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\nslope: \\(\\frac{4}{3}\\)<br \/>\ny-intercept: 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44978\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-Question-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 Question 55\" width=\"250\" height=\"168\" \/><\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_Performance_Task:_Prize_Patrol\"><\/a>Solving Systems of Linear Equations Performance Task: Prize Patrol<\/h3>\n<p><strong>5.5\u20135.7 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 21\" width=\"645\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-21.png 645w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-21-300x42.png 300w\" sizes=\"(max-width: 645px) 100vw, 645px\" \/><\/p>\n<p><strong>Core Concepts<\/strong><br \/>\nSection 5.5<br \/>\nSolving Linear Equations by Graphing, p. 262<br \/>\nSolving Absolute Value Equations by Graphing, p. 263<\/p>\n<p>Section 5.6<br \/>\nGraphing a Linear Inequality in Two Variables, p. 269<\/p>\n<p>Section 5.7<br \/>\nGraphing a System of Linear Inequalities, p. 275<br \/>\nWriting a System of Linear Inequalities, p. 276<\/p>\n<p><strong>Mathematical Practices<\/strong><\/p>\n<p>Question 1.<br \/>\nWhy do the equations in Exercise 35 on page 266 contain absolute value expressions?<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nWhy is it important to be precise when answering part (a) of Exercise 39 on page 272?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nDescribe the overall step-by-step process you used to solve Exercise 35 on page 279.<br \/>\nAnswer:<\/p>\n<p><strong>Performance Task Prize Patrol<\/strong><\/p>\n<p>You have been selected to drive a prize patrol cart and place prizes on the competing teams\u2019 predetermined paths. You know the teams\u2019 routes and you can only make one pass. Where will you place the prizes so that each team will have a chance to find a prize on their route?<br \/>\nTo explore the answers to these questions and more, go to<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-22.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations 5.7 22\" width=\"380\" height=\"286\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-22.png 380w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations-5.7-22-300x226.png 300w\" sizes=\"(max-width: 380px) 100vw, 380px\" \/><\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_Chapter_Review\"><\/a>Solving Systems of Linear Equations Chapter Review<\/h3>\n<p><strong>5.1 Solving Systems of Linear Equations by Graphing (pp. 235\u2013240)<\/strong><\/p>\n<p><strong>Solve the system of linear equations by graphing.<\/strong><br \/>\nQuestion 1.<br \/>\ny = -3x + 1<br \/>\ny = x &#8211; 7<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ny = -4x + 3<br \/>\n4x &#8211; 2y = 6<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n5x + 5y = 15<br \/>\n2x &#8211; 2y = 10<br \/>\nAnswer:<\/p>\n<p><strong>5.2 Solving Systems of Linear Equations by Substitution (pp. 241\u2013246)<\/strong><\/p>\n<p><strong>Solve the system of linear equations by substitution. Check your solution.<\/strong><br \/>\nQuestion 4.<br \/>\n3x + y = -9<br \/>\ny = 5x + 7<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nx + 4y = 6<br \/>\nx &#8211; y = 1<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n2x + 3y = 4<br \/>\ny + 3x = 6<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nYou spend $20 total on tubes of paint and disposable brushes for an art project. Tubes of paint cost $4.00 each and paintbrushes cost $0.50 each. You purchase twice as many brushes as tubes of paint. How many brushes and tubes of paint do you purchase?<br \/>\nAnswer:<\/p>\n<p><strong>5.3 Solving Systems of Linear Equations by Elimination (pp. 247 \u2013 252)<\/strong><\/p>\n<p><strong>Solve the system of linear equations by elimination. Check your solution.<\/strong><br \/>\nQuestion 8.<br \/>\n9x &#8211; 2y = 34<br \/>\n5x + 2y = -6<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nx + 6y = 28<br \/>\n2x &#8211; 3y = -19<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n8x &#8211; 7y = -3<br \/>\n6x &#8211; 5y = -1<br \/>\nAnswer:<\/p>\n<p><strong>5.4 Solving Special Systems of Linear Equations (pp. 253\u2013258)<\/strong><\/p>\n<p><strong>Solve the system of linear equations.<\/strong><br \/>\nQuestion 11.<br \/>\nx = y + 2<br \/>\n-3x + 3y = 6<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n3x &#8211; 6y = -9<br \/>\n-5x + 10y = 10<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n-4x + 4y = 32<br \/>\n3x + 24 = 3y<br \/>\nAnswer:<\/p>\n<p><strong>5.5 Solving Equations by Graphing (pp. 261\u201326<\/strong><\/p>\n<p><strong>Solve the equation by graphing. Check your solution(s).<\/strong><br \/>\nQuestion 14.<br \/>\n\\(\\frac{1}{3}\\)x + 5 = -2x &#8211; 2<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n|x + 1| = |-x &#8211; 9|<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\n|2x &#8211; 8| = |x + 5|<br \/>\nAnswer:<\/p>\n<p><strong>5.6 Graphing Linear Inequalities in Two Variables (pp. 267\u2013272)<\/strong><\/p>\n<p><strong>Graph the inequality in a coordinate plane.<\/strong><br \/>\nQuestion 17.<br \/>\ny &gt; -4<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n-9x + 3y \u2265 3<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n5x + 10y &lt; 40 Answer: 5.7 Systems of Linear Inequalities (pp. 273\u2013280) Graph the system of linear inequalities. Question 20. y \u2264 x &#8211; 3 y \u2265 x + 1 Answer: Question 21. y &gt; -2x + 3<br \/>\ny \u2265 \\(\\frac{1}{4}\\)x &#8211; 1<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\nx + 3y &gt; 6<br \/>\n2x + y &lt; 7<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_Chapter_Test\"><\/a>Solving Systems of Linear Equations Chapter Test<\/h3>\n<p><strong>Solve the system of linear equations using any method. Explain why you chose the method. <\/strong><\/p>\n<p>Question 1.<br \/>\n8x + 3y = -9<br \/>\n-8x + y = 29<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{1}{2}\\)x + y = -6<br \/>\ny = \\(\\frac{3}{5}\\)x + 5<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ny = 4x + 4<br \/>\n-8x + 2y = 8<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nx = y &#8211; 11<br \/>\nx &#8211; 3y = 1<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n6x &#8211; 4y = 9<br \/>\n9x &#8211; 6y = 15<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\ny = 5x &#8211; 7<br \/>\n-4x + y = -1<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nWrite a system of linear inequalities so the points (1, 2) and (4, -3) are solutions of the system, but the point (-2, 8) is not a solution of the system.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nHow is solving the equation |2x + 1| = |x &#8211; 7| by graphing similar to solving the equation 4x + 3 = -2x + 9 by graphing? How is it different?<br \/>\nAnswer:<\/p>\n<p><strong>Graph the system of linear inequalities.<\/strong><br \/>\nQuestion 9.<br \/>\ny &gt; \\(\\frac{1}{2}\\)x + 4<br \/>\n2y \u2264 x + 4<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nx + y &lt; 1 5x + y &gt; 4<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\ny \u2265 &#8211; \\(\\frac{2}{3}\\)x + 1<br \/>\n-3x + y &gt; -2<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nYou pay $45.50 for 10 gallons of gasoline and 2 quarts of oil at a gas station. Your friend pays $22.75 for 5 gallons of the same gasoline and 1 quart of the same oil.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ct-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations ct 1\" width=\"224\" height=\"238\" \/><br \/>\na. Is there enough information to determine the cost of 1 gallon of gasoline and 1 quart of oil? Explain.<br \/>\nb. The receipt shown is for buying the same gasoline and same oil. Is there now enough information to determine the cost of 1 gallon of gasoline and 1 quart of oil? Explain.<br \/>\nc. Determine the cost of 1 gallon of gasoline and 1 quart of oil.<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nDescribe the advantages and disadvantages of solving a system of linear equations by graphing.<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nYou have at most $60 to spend on trophies and medals to give as prizes for a contest.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ct-2.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations ct 2\" width=\"279\" height=\"189\" \/><br \/>\na. Write and graph an inequality that represents the numbers of trophies and medals you can buy. Identify and interpret a solution of the inequality.<br \/>\nb. You want to purchase at least 6 items. Write and graph a system that represents the situation. How many of each item can you buy?<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nCompare the slopes and y-intercepts of the graphs of the equations in the linear system 8x + 4y = 12 and 3y = -6x &#8211; 15 to determine whether the system has one solution, no solution, or infinitely many solutions. Explain.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_Cumulative_Assessment\"><\/a>Solving Systems of Linear Equations Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nThe graph of which equation is shown?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations ca 1\" width=\"569\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-1.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-1-300x91.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nA van rental company rents out 6-, 8-, 12-, and 16-passenger vans. The function C(x) = 100 + 5x represents the cost C (in dollars) of renting an x-passenger van for a day. Choose the numbers that are in the range of the function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-2.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations ca 2\" width=\"387\" height=\"48\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-2.png 387w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-2-300x37.png 300w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nFill in the system of linear inequalities with &lt;, \u2264, &gt;, or \u2265 so that the graph represents the system.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations ca 3\" width=\"407\" height=\"154\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-3.png 407w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-3-300x114.png 300w\" sizes=\"(max-width: 407px) 100vw, 407px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nYour friend claims to be able to fill in each box with a constant so that when you set each side of the equation equal to y and graph the resulting equations, the lines will intersect exactly once. Do you support your friend\u2019s claim? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-4.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations ca 4\" width=\"160\" height=\"51\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nSelect the phrases you should use when describing the transformations from the graph of f to the graph of g.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations ca 5\" width=\"593\" height=\"154\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-5.png 593w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-5-300x78.png 300w\" sizes=\"(max-width: 593px) 100vw, 593px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nWhich two equations form a system of linear equations that has no solution?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-6.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations ca 6\" width=\"464\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-6.png 464w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-6-300x39.png 300w\" sizes=\"(max-width: 464px) 100vw, 464px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nFill in a value for a so that each statement is true for the equation ax &#8211; 8 = 4 &#8211; x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-7.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations ca 7\" width=\"285\" height=\"92\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nWhich ordered pair is a solution of the linear inequality whose graph is shown?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-8.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations ca 8\" width=\"400\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-8.png 400w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-8-300x122.png 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nWhich of the systems of linear equations are equivalent?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-9.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations ca 9\" width=\"545\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-9.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-9-300x39.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nThe value of x is more than 9. Which of the inequalities correctly describe the triangle? The perimeter (in feet) is represented by P, and the area (in square feet) is represented by A.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-37015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-10.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 5 Solving Systems of Linear Equations ca 10\" width=\"585\" height=\"210\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-10.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-5-Solving-Systems-of-Linear-Equations-ca-10-300x108.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><br \/>\nAnswer:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Want to become Math Proficient in the future? Then, practice the questions of Ch 5 Solving Systems of Linear Equations from the BIM Algebra 1 Solution Key is the best choice. Also, kids can move on the right track by solving the textbook questions covered in Big Ideas Math Algebra 1 Answers Chapter 5 Solving &#8230; <a title=\"Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers-chapter-5\/\" aria-label=\"More on Big Ideas Math Algebra 1 Answers Chapter 5 Solving Systems of Linear Equations\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":89187,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-5-Solving-Systems-of-Linear-Equations.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/36909"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=36909"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/36909\/revisions"}],"predecessor-version":[{"id":90363,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/36909\/revisions\/90363"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89187"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=36909"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=36909"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=36909"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}