{"id":32517,"date":"2022-04-04T11:59:50","date_gmt":"2022-04-04T06:29:50","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=32517"},"modified":"2022-04-07T11:39:34","modified_gmt":"2022-04-07T06:09:34","slug":"big-ideas-math-answers-grade-8-chapter-5","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-8-chapter-5\/","title":{"rendered":"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations"},"content":{"rendered":"<p>Big Ideas Math Answers Grade 8 Chapter 5 include questions on System of Linear Equations by Graphing, Substitution, Elimination, Connecting Concepts, etc. All the Problems in the Big Ideas Grade 8 Ch 5 System of Linear Equations are provided in a simple and easy-to-understand language. Learn the problem-solving methods used by referring to our <strong>Big Ideas Math Grade 8 Answers<\/strong> Chapter 5 System of Linear Equations and apply them to similar kinds of problems. Download the BIM Chapter 5 System of Linear Equations Answer Key and understand the related concepts in no time.<\/p>\n<h2>Big Ideas Math Book 8th Grade Answer Key Chapter 5 Systems of Linear Equations<\/h2>\n<p>Big Ideas Math Answers Grade 8 Ch 5 is curated by subject experts adhering to the latest syllabus guidelines. Practice as many times as possible and attempt the exams with utmost confidence and score well. Enhance your subject knowledge and gain a deeper understanding of concepts at the surface level. Simply click on the direct links available and begin preparing the respective topics in no time.<\/p>\n<p><strong>Performance<\/strong><\/p>\n<ul>\n<li><a href=\"#Systems_of_Linear_Equations_STEAM_Video\/Performance\">Systems of Linear Equations STEAM Video\/Performance<\/a><\/li>\n<li><a href=\"#Systems_of_Linear_Equations_Getting_Ready_for_Chapter_5\">Systems of Linear Equations Getting Ready for Chapter 5<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Solving Systems of Linear Equations by Graphing<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.1_Solving_Systems_of_Linear_Equations_by_Graphing\">Lesson 5.1 Solving Systems of Linear Equations by Graphing<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_by_Graphing_Homework_&amp;_Practice_5.1\">Solving Systems of Linear Equations by Graphing Homework &amp; Practice 5.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Solving Systems of Linear Equations by Substitution<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.2_Solving_Systems_of_Linear_Equations_by_Substitution\">Lesson 5.2 Solving Systems of Linear Equations by Substitution<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_by_Substitution_Homework_&amp;_Practice_5.2\">Solving Systems of Linear Equations by Substitution Homework &amp; Practice 5.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Solving Systems of Linear Equations by Elimination<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.3_Solving_Systems_of_Linear_Equations_by_Elimination\">Lesson 5.3 Solving Systems of Linear Equations by Elimination<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_by_Elimination_Homework_&amp;_Practice_5.3\">Solving Systems of Linear Equations by Elimination Homework &amp; Practice 5.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Solving Special Systems of Linear Equations<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_5.4_Solving_Special_Systems_of_Linear_Equations\">Lesson 5.4 Solving Special Systems of Linear Equations<\/a><\/li>\n<li><a href=\"#Solving_Special_Systems_of_Linear_Equations_Homework_&amp;_Practice_5.4\">Solving Special Systems of Linear Equations Homework &amp; Practice 5.4<\/a><\/li>\n<\/ul>\n<p><strong>Chapter: 5 &#8211; Systems of Linear Equations<\/strong><\/p>\n<ul>\n<li><a href=\"#Systems_of_Linear_Equations_Connecting_Concepts\">Systems of Linear Equations Connecting Concepts<\/a><\/li>\n<li><a href=\"#Systems_of_Linear_Equations_Chapter_Review\">Systems of Linear Equations Chapter Review<\/a><\/li>\n<li><a href=\"#Systems_of_Linear_Equations_Practice_Test\">Systems of Linear Equations Practice Test<\/a><\/li>\n<li><a href=\"#Systems_of_Linear_Equations_Cumulative_Practice\">Systems of Linear Equations Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Systems_of_Linear_Equations_STEAM_Video\/Performance\"><\/a>Systems of Linear Equations STEAM Video\/Performance<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p><strong>Gold Alloys<\/strong><\/p>\n<p>An alloy is a mixture of different metals melted together at high temperatures. A dental \ufb01lling is created using a gold alloy. What are other uses of alloys?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32610\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-1.1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 1.1\" width=\"188\" height=\"230\" \/><\/p>\n<p><strong>Watch the STEAM Video \u201cGold Alloys.\u201d Then answer the following questions.<\/strong><\/p>\n<p>Question 1.<br \/>\nEnid says that the proportion of gold in an alloy can be measured in karats. For example, 24 karats represent 100% gold and 18 karats represent 75% gold.<br \/>\na. A dental \ufb01lling is 9 karats. What percent of the \ufb01lling is gold?<br \/>\nb. A watch is 60% gold. How many karats is the watch?<\/p>\n<p>Answer:<br \/>\na. 37.5% of the filling is gold.<br \/>\nb. 14.4 karats are the watch<\/p>\n<p>Explanation:<br \/>\na. A dental \ufb01lling is 9 karats.<br \/>\n24 karats represent 100% gold<br \/>\nSo, 9 karats = (100 * 9)\/24<br \/>\n= 900\/24<br \/>\n= 37.5%<br \/>\n37.5% of the filling is gold.<br \/>\nb. A watch is 60% gold<br \/>\n24 karats represent 100% gold<br \/>\nSo, watch = (60 * 24)\/100<br \/>\n= 1440\/100<br \/>\n= 14.4<br \/>\n14.4 karats are the watch<\/p>\n<p>Question 2.<br \/>\nWhat percent gold is each described alloy?<br \/>\na. A mixture of 2 grams 10-karat gold and 2 grams 14-karat gold<br \/>\nb. A mixture of 6 grams 24-karat gold and 4 grams 9-karat gold<\/p>\n<p>Answer:<br \/>\na. 200%<br \/>\nb. 750%<\/p>\n<p>Explanation:<br \/>\na. 24 karats represents 100% gold<br \/>\n10 karat gold is 125\/3 %<br \/>\n14 -karat gold gold is 175\/3 %<br \/>\n2 grams 10-karat gold = 2(125\/3) = 250\/3<br \/>\n2 grams 14-karat gold = 2(175\/3) = 350\/3<br \/>\nThe alloy mixture = (250 + 350)\/3<br \/>\n= 600\/3 = 200<br \/>\nb. 6 grams 24-karat gold<br \/>\n6 grams = 600%<br \/>\n9-karat gold = 75\/2<br \/>\n4 grams 9-karat gold = 4(75)\/2 = 150%<br \/>\nThe alloy mixture = 600% + 150% = 750%<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Mixing Alloys<\/strong><\/p>\n<p>After completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will be given a list of gold alloys available at a jewelry store.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32611\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-1.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 1\" width=\"183\" height=\"132\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32547\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-2.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 2\" width=\"288\" height=\"364\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-2.png 288w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-2-237x300.png 237w\" sizes=\"(max-width: 288px) 100vw, 288px\" \/><br \/>\nYou will use a system of equations to determine the amounts of the given alloys that a jeweler needs to create a new alloy. Why might a jeweler need to create a mixture with a speci\ufb01c proportion of gold?<\/p>\n<h3><a id=\"Systems_of_Linear_Equations_Getting_Ready_for_Chapter_5\"><\/a>Systems of Linear Equations Getting Ready for Chapter 5<\/h3>\n<p><strong>Getting Ready for Chapter 5<\/strong><\/p>\n<p><strong>Chapter Exploration<\/strong><\/p>\n<p>Question 1.<br \/>\nWork with a partner. Your family starts a bed-and-breakfast. You spend $500 \ufb01xing up a bedroom to rent. The cost for food and utilities is $10 per night. Your family charges $60 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-32548\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-3.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 3\" width=\"383\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-3.png 383w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-3-300x49.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><br \/>\nb. Write an equation that represents the revenue (income).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32549\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-4.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 4\" width=\"298\" height=\"63\" \/><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>Answer:<br \/>\na. C = 10x + 500<br \/>\nb. R = 60x<br \/>\nc. The system of linear equations are<br \/>\nC = 10x + 500<br \/>\nR = 60x<\/p>\n<p>Explanation:<br \/>\na. Cost, C = $10 per night . Number of nights, x + $500<br \/>\nC = 10x + 500<br \/>\nb.<br \/>\nRevenue, R = $60 per night . Number of nights x<br \/>\nR = 60x<br \/>\nc. The system of linear equations are<br \/>\nC = 10x + 500<br \/>\nR = 60x<\/p>\n<p>Question 2.<br \/>\n<strong>Work with a partner. Use a graphing calculator to solve the system.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32550\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-5.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 5\" width=\"225\" height=\"60\" \/><br \/>\na. Enter the equations into your calculator. Then graph the equations. What is an appropriate window?<br \/>\nb. On your graph, how can you determine which line is the graph of which equation? Label the equations on the graph shown.<br \/>\nc. Visually estimate the point of intersection of the graphs.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32551\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-6.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 6\" width=\"200\" height=\"162\" \/><br \/>\nd. To \ufb01nd the solution, use the intersect feature to \ufb01nd the point of intersection. The solution is <img loading=\"lazy\" class=\"alignnone size-full wp-image-32553\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-7.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 7\" width=\"95\" height=\"37\" \/><\/p>\n<p>Answer:<br \/>\nThe solution is (10, 600)<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations.jpg\" alt=\" Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations\" width=\"554\" height=\"539\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations.jpg 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-300x292.jpg 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><br \/>\nThe solution is (10, 600)<\/p>\n<p><strong>Vocabulary<\/strong><\/p>\n<p>The following vocabulary terms are de\ufb01ned in this chapter. Think about what each term might mean and record your thoughts.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32552\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-7.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 7.1\" width=\"560\" height=\"36\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-7.1.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-7.1-300x19.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/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>EXPLORATION 1<\/strong><br \/>\n<strong>Work with a partner. You charge your headphones and your phone. The equations below represent the battery powers p% of the devices after x minutes of charging.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32555\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-8.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 8\" width=\"209\" height=\"85\" \/><br \/>\na. You check the battery power of each device every 10 minutes. Copy and complete the table. How do the devices\u2019 battery powers compare?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-8.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 8.1\" width=\"435\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-8.1.png 435w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-8.1-300x75.png 300w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><br \/>\nb. After how much time do the devices have the same battery power? What is the battery power at that time? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32556\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-9.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 9\" width=\"338\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-9.png 338w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-9-300x174.png 300w\" sizes=\"(max-width: 338px) 100vw, 338px\" \/><br \/>\nc. The solutions of a linear equation are all the points on its graph. How many solutions can two linear equations share? Explain your reasoning.<br \/>\nd. Graph the battery power equations in the same coordinate plane. What do you notice?<br \/>\ne. Use a graphing calculator to check your answers in part(b). Explain your method.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32557\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-10.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 10\" width=\"156\" height=\"191\" \/><\/p>\n<p>Answer:<br \/>\na. <img loading=\"lazy\" class=\"alignnone size-full wp-image-49837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-30.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 30\" width=\"426\" height=\"107\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-30.jpg 426w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-30-300x75.jpg 300w\" sizes=\"(max-width: 426px) 100vw, 426px\" \/><br \/>\nd. The solution is (75\/2, 125\/2)<\/p>\n<p>Explanation:<br \/>\na. Headphones equation is p = 5\/3 x<br \/>\np1 = 5\/3 (10) = 50\/3, p2 = 5\/3 (20) = 100\/3, p3 = 5\/3 (30) = 50, p4 = 5\/3 (40) = 200\/3, p5 = 5\/3 (50) = 250\/3<br \/>\np6 = 5\/3 (60) = 100<br \/>\nPhone equation is p = x + 25<br \/>\np1 = 10 + 25 = 35, p2 = 20 + 25 = 45, p3 = 30 + 25 = 55, p4 = 40 + 25 = 65<br \/>\np5 = 50 + 25 = 75, p6 = 60 + 25 = 85<br \/>\nb. <img loading=\"lazy\" class=\"alignnone size-full wp-image-49843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-31.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 31\" width=\"544\" height=\"538\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-31.jpg 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-31-300x297.jpg 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><br \/>\nThe solution is (75\/2, 125\/2)<br \/>\np = 5\/3 x, p = x + 25<br \/>\nPut x = 75\/2<br \/>\np = 5\/3 (75\/2)<br \/>\n= 125\/2<br \/>\np = 75\/2 + 25<br \/>\n= 125\/2<\/p>\n<p><strong>5.1 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the system by graphing.<\/strong><\/p>\n<p>Question 1.<br \/>\ny = x &#8211; 1<br \/>\ny\u00a0 = -x + 3<\/p>\n<p>Answer:<br \/>\nThe solution is (1, 2).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = x &#8211; 1, y\u00a0 = -x + 3<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49519\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-1.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 1\" width=\"511\" height=\"515\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-1.jpg 511w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-1-298x300.jpg 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-1-150x150.jpg 150w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><br \/>\nThe graphs appear to intersect at (1, 2)<br \/>\nSo, the solution is (1, 2)<\/p>\n<p>Question 2.<br \/>\ny = -5x + 14<br \/>\ny = x &#8211; 10<\/p>\n<p>Answer:<br \/>\nThe solution is (4, -6)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = -5x + 14, y = x &#8211; 10<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49521\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-2.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 2\" width=\"547\" height=\"542\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-2.jpg 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-2-300x297.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-2-150x150.jpg 150w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><br \/>\nThe lines intersect at (4, -6)<br \/>\nSo, the solution is (4, -6)<\/p>\n<p><span style=\"font-size: 16px;\">Question 3.<br \/>\n<\/span>y = x<br \/>\ny = 2x + 1<\/p>\n<p>Answer:<br \/>\nThe solution is (-1, -1)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = x, y = 2x + 1<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49522\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-3.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 3\" width=\"536\" height=\"532\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-3.jpg 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-3-300x298.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-3-150x150.jpg 150w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><br \/>\nThe lines intersect at (-1, -1)<br \/>\nSo, the solution is (-1, -1)<\/p>\n<p>Question 4.<br \/>\ny = -4x &#8211; 7<br \/>\nx + y = 2<\/p>\n<p>Answer:<br \/>\nThe solution is (-3, 5)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = -4x &#8211; 7, x + y = 2<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49525\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-4.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 4\" width=\"531\" height=\"531\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-4.jpg 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-4-300x300.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-4-150x150.jpg 150w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><br \/>\nThe lines intersect at (-3, 5)<br \/>\nSo, the solution is (-3, 5)<\/p>\n<p>Question 5.<br \/>\nx &#8211; y = 5<br \/>\n-3x +\u00a0 y = -1<\/p>\n<p>Answer:<br \/>\nThe solution is (-2, -7)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are x &#8211; y = 5, -3x +\u00a0 y = -1<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49526\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-5.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 5\" width=\"528\" height=\"531\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-5.jpg 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-5-298x300.jpg 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-5-150x150.jpg 150w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><br \/>\nThe lines intersect at (-2, -7)<br \/>\nSo, the solution is (-2, -7)<\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32558\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-16.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 16\" width=\"105\" height=\"69\" \/><\/p>\n<p>Answer:<br \/>\nThe solution is (4, -8)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are 1\/2 x + y = -6, 6x + 2y = 8<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49527\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-7.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 7\" width=\"523\" height=\"520\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-7.jpg 523w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-7-300x298.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-7-150x150.jpg 150w\" sizes=\"(max-width: 523px) 100vw, 523px\" \/><br \/>\nThe lines intersect at (4, -8)<br \/>\nSo, the solution is (4, -8)<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>SOLVING A SYSTEM OF LINEAR EQUATIONS<\/strong><br \/>\n<strong>Solve the system by graphing.<\/strong><\/p>\n<p>Question 7.<br \/>\ny = x + 1<br \/>\ny = 4x +1<\/p>\n<p>Answer:<br \/>\nThe solution is (0, 1).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = x + 1, y = 4x +1<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49529\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-8.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 8\" width=\"533\" height=\"527\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-8.jpg 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-8-300x297.jpg 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><br \/>\nThe lines intersect at (0, 1)<br \/>\nSo, the solution is (0, 1)<\/p>\n<p>Question 8.<br \/>\n3x &#8211; y = -1<br \/>\ny = -x + 5<\/p>\n<p>Answer:<br \/>\nThe solution is (1, 4).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are 3x &#8211; y = -1, y = -x + 5<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49530\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-9.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 9\" width=\"532\" height=\"533\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-9.jpg 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-9-300x300.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-9-150x150.jpg 150w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><br \/>\nThe lines intersect at (1, 4)<br \/>\nSo, the solution is (1, 4).<\/p>\n<p>Question 9.<br \/>\nx + 2y = 3<br \/>\n-x + 3y = 7<\/p>\n<p>Answer:<br \/>\nThe solution is (-1, 2).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are x + 2y = 3, -x + 3y = 7<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49531\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-10.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 10\" width=\"542\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-10.jpg 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-10-300x290.jpg 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><br \/>\nThe lines intersect at (-1, 2)<br \/>\nSo, the solution is (-1, 2).<\/p>\n<p>Question 10.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain why the solution of a system of linear equations is the point of intersection of their graphs.<\/p>\n<p>Answer:<br \/>\nThe solution of a system of linear equations in two variables is an ordered pair that is a solution of each equation in the system. The ordered pair is obtained by drawing a graph for two equations and the point of intersection.<\/p>\n<p>Question 11.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32559\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-20.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 20\" width=\"686\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-20.png 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-20-300x70.png 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Answer:<br \/>\nThe solution of the system is (1, 6)<br \/>\nThe graphs of the equations intersect at (1, 6)<br \/>\nOrdered pair (1, 6) makes both equations true<\/p>\n<p>Explanation:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-32.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 32\" width=\"529\" height=\"534\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-32.jpg 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-32-297x300.jpg 297w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-32-150x150.jpg 150w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><br \/>\nThe point of intersection is the solution.<br \/>\nThe solution is (1, 6).<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 12.<br \/>\nYour family attends a comic convention. Each autograph costs $20 and each photograph costs $50. Your family buys a total of 5 autographs and photographs for $160. How many photographs does your family buy?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32561\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-21.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 21\" width=\"211\" height=\"289\" \/><\/p>\n<p>Answer:<br \/>\nThe number of photographs the family buys will be 2.<\/p>\n<p>Explanation:<br \/>\nEach autograph costs $20 and photograph costs $50<br \/>\nAccording to the question, the family buys a total of 5 items including both autographs and photographs for $160.<br \/>\nLet&#8217;s assume the number of autographs bought be x, while the number of photographs is 5 &#8211; x<br \/>\nThus, cost to buy autographs will be 20* x = 20x and photographs will be 50(5 &#8211; x) = 250 &#8211; 50x<br \/>\nnow, total cost becomes 20x + 250 &#8211; 50x, which will be equal to 160. lets find number of each items x<br \/>\n20x + 250 &#8211; 50x = 160<br \/>\n-30x = 160 &#8211; 250<br \/>\n-30x = -90<br \/>\nx = 3<br \/>\nHence, the cost of buying autographs will be $20 * 3 = $60 and the cost to buy photographs will be (250 &#8211; 50) * 3 = 250 &#8211; 150 = $100<br \/>\nThe number of photographs the family buys will be 5 &#8211; 3 = 2<\/p>\n<p>Question 13.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nTwo apps on your phone take away points for using your phone at school. You have 140 points on the \ufb01rst app and 80 points on the second app when a school day begins. Each time you check your phone, you lose 10 points on your \ufb01rst app and p points on your second app. After you check your phone ten times, you have the same number of points on each app. Find the value of p.<\/p>\n<p>Answer:<br \/>\np = 4<\/p>\n<p>Explanation:<br \/>\nApp one has 140 points and 80 points on the second app<br \/>\nAs per the question, app one loses 10 points for each check while app second loses p points. We check the phone 10 times<br \/>\nSo, total points lost by app 1 will be 10 * 10 = 100, and points lost by app 2 will be p * 10 = 10p<br \/>\nAfter 10 times both apps are left with the same points.<br \/>\nSo let&#8217;s find the value of p<br \/>\nThus, points left in the first app will be 140 &#8211; 100 = 40 while in the second app will be 80 &#8211; 10p<br \/>\n40 = 80 &#8211; 10p<br \/>\n10p = 80 &#8211; 40<br \/>\n10p = 40<br \/>\np = 40\/10<br \/>\np = 4<\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_by_Graphing_Homework_&amp;_Practice_5.1\"><\/a>Solving Systems of Linear Equations by Graphing Homework &amp; Practice 5.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Write an equation in point-slope form of the line that passes through the given point and has the given slope.<\/strong><\/p>\n<p>Question 1.<br \/>\n(3, -4); m = 1<\/p>\n<p>Answer:<br \/>\ny = x &#8211; 7<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n(3, -4); m = 1<br \/>\nx\u2081 = 3, y\u2081 = -4<br \/>\nSlope intercept form of a line is (y &#8211; y\u2081) = m(x &#8211; x\u2081)<br \/>\nTherefore, (y &#8211; (-4)) = 1(x &#8211; 3)<br \/>\n(y + 4) = (x &#8211; 3)<br \/>\ny = x &#8211; 3 &#8211; 4<br \/>\ny = x &#8211; 7<\/p>\n<p>Question 2.<br \/>\n(5, 6); m = \\(\\frac{3}{5}\\)<\/p>\n<p>Answer:<br \/>\n5y = 3x + 15<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n(5, 6); m = \\(\\frac{3}{5}\\)<br \/>\nx\u2081 = 5, y\u2081 = 6<br \/>\nSlope intercept form of a line is (y &#8211; y\u2081) = m(x &#8211; x\u2081)<br \/>\nTherefore, (y &#8211; 6) = 3\/5(x &#8211; 5)<br \/>\n5(y &#8211; 6) = 3(x &#8211; 5)<br \/>\n5y &#8211; 30 = 3x &#8211; 15<br \/>\n5y = 3x &#8211; 15 + 30<br \/>\n5y = 3x + 15<\/p>\n<p>Question 3.<br \/>\n(1, 10); m = &#8211;\\(\\frac{1}{4}\\)<\/p>\n<p>Answer:<br \/>\n4y = 41 &#8211; x<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n(1, 10); m = &#8211;\\(\\frac{1}{4}\\)<br \/>\nx\u2081 = 1, y\u2081 = 10<br \/>\nSlope intercept form of a line is (y &#8211; y\u2081) = m(x &#8211; x\u2081)<br \/>\nTherefore, (y &#8211; 10) = -1\/4(x &#8211; 1)<br \/>\n4(y &#8211; 10) = -1(x &#8211; 1)<br \/>\n4y &#8211; 40 = -x + 1<br \/>\n4y = -x + 1 + 40<br \/>\n4y = 41 &#8211; x<\/p>\n<p>Solve the equation. Check your solution<\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32560\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-21.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 21.1\" width=\"121\" height=\"49\" \/><\/p>\n<p>Answer:<br \/>\nc = 8<\/p>\n<p>Explanation:<br \/>\nGiven equation is 3\/4 c &#8211; 1\/4 c + 3 = 7<br \/>\n2\/4 c + 3 = 7<br \/>\n1\/2 c = 7 &#8211; 3<br \/>\n1\/2 c = 4<br \/>\nc = 4 * 2<br \/>\nc = 8<br \/>\nSubstituting c = 8 in 3\/4 c &#8211; 1\/4 c + 3 = 7<br \/>\n3\/4 (8) &#8211; 1\/4 (8) + 3 = 6 &#8211; 2 + 3<br \/>\n= 9 &#8211; 2 = 7<\/p>\n<p>Question 5.<br \/>\n5(2 &#8211; y) + y = -6<\/p>\n<p>Answer:<br \/>\ny = 4<\/p>\n<p>Explanation:<br \/>\nGiven equation is 5(2 &#8211; y) + y = -6<br \/>\n10 &#8211; 5y + y = -6<br \/>\n10 &#8211; 4y = -6<br \/>\n10 + 6 = 4y<br \/>\n4y = 16<br \/>\ny = 16\/4<br \/>\ny = 4<br \/>\nSubstituting y = 4 in 5(2 &#8211; y) + y = -6<br \/>\n5(2 &#8211; 4) + 4 = 5(-2) + 4<br \/>\n= -10 + 4 = -6<\/p>\n<p>Question 6.<br \/>\n6x &#8211; 3(x + 8) = 9<\/p>\n<p>Answer:<br \/>\nx = 11<\/p>\n<p>Explanation:<br \/>\nGiven equation is 6x &#8211; 3(x + 8) = 9<br \/>\n6x &#8211; 3x &#8211; 24 = 9<br \/>\n3x &#8211; 24 = 9<br \/>\n3x = 9 + 24<br \/>\n3x = 33<br \/>\nx = 33\/3<br \/>\nx = 11<br \/>\nSubstituting x = 11 in 6x &#8211; 3(x + 8) = 9<br \/>\n6(11) &#8211; 3(11 + 8) = 66 &#8211; 3(19)<br \/>\n= 66 &#8211; 57 = 9<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><br \/>\n<strong>USING A GRAPH TO SOLVE A PROBLEM<\/strong><br \/>\n<strong>The equations below represent the numbers y of tickets sold after x weeks for two different local music festivals.<\/strong> (See Exploration 1, p. 199.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32562\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-22.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 22\" width=\"321\" height=\"94\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-22.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-22-300x88.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><\/p>\n<p>Question 7.<br \/>\nYou check the ticket sales for both festivals each week for 10 weeks. Create a table for the ticket sales each week. How do the festivals\u2019 ticket sales compare?<\/p>\n<p>Answer:<br \/>\nWe can say that tickets for the country Music Festival sold more by mid the 4th week. After the mid of 4th-week tickets for the Pop Music Festival sold more than the country music festival.<\/p>\n<p>Explanation:<br \/>\nTicket sales for a country music festival and pop music festival are calculated in the tables below for 10 weeks<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-33.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 33\" width=\"734\" height=\"480\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-33.jpg 734w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-33-300x196.jpg 300w\" sizes=\"(max-width: 734px) 100vw, 734px\" \/><br \/>\nFrom the above tables, we can say that tickets for the country Music Festival sold more by mid of the 4th week. After the mid of 4th-week tickets for the Pop Music Festival sold more than the country music festival.<\/p>\n<p>Question 8.<br \/>\nAfter how much time have the same number of tickets been sold for both festivals? What is the number of tickets sold at that time?<\/p>\n<p>Answer:<br \/>\nThe number of tickets sold for both festivals each is 185.<\/p>\n<p>Explanation:<br \/>\nCountry music festival y = 10x + 150<br \/>\nPop musuic festival y = 20x + 115<br \/>\nAs per the question, we will equate both the equation to get x value<br \/>\n10x + 150 = 20x + 115<br \/>\n10x &#8211; 20x = 115 &#8211; 150<br \/>\n-10x = -35<br \/>\nx = 35\/10<br \/>\nx = 3.5<br \/>\nThus, we get 3.5 weeks after which both festivals would sold equal number of tickets.<br \/>\nLet us find the number of tickets at that time<br \/>\nPut x = 3.5 in y = 10x + 150<br \/>\ny = 10(3.5) + 150<br \/>\n= 35 + 150 = 185<br \/>\nHence, the number of tickets sold for both festivals each are 185.<\/p>\n<p><strong>SOLVING A SYSTEM OF LINEAR EQUATIONS<\/strong><br \/>\n<strong>Solve the system by graphing.<\/strong><\/p>\n<p>Question 9.<br \/>\ny = 2x + 9<br \/>\ny = 6 &#8211; x<\/p>\n<p>Answer:<br \/>\nThe solution is (-1, 7)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = 2x + 9, y = 6 &#8211; x<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49534\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-11.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 11\" width=\"529\" height=\"534\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-11.jpg 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-11-297x300.jpg 297w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-11-150x150.jpg 150w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><br \/>\nThe lines intersect at (-1, 7)<br \/>\nSo, the solution is (-1, 7)<\/p>\n<p>Question 10.<br \/>\ny = -x &#8211; 4<br \/>\ny = \\(\\frac{3}{5}\\)x + 4<\/p>\n<p>Answer:<br \/>\nThe solution is (-5, 1).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = -x &#8211; 4, y = \\(\\frac{3}{5}\\)x + 4<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49535\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-12.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 12\" width=\"527\" height=\"520\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-12.jpg 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-12-300x296.jpg 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><br \/>\nThe lines intersect at<br \/>\nSo, the solution is (-5, 1)<\/p>\n<p>Question 11.<br \/>\ny = 2x + 5<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 1<\/p>\n<p>Answer:<br \/>\nThe solution is (-4, -3).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = 2x + 5, y = \\(\\frac{1}{2}\\)x &#8211; 1<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49537\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-13.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 13\" width=\"537\" height=\"534\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-13.jpg 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-13-300x298.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-13-150x150.jpg 150w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><br \/>\nThe lines intersect at (-4, -3)<br \/>\nSo, the solution is (-4, -3).<\/p>\n<p>Question 12.<br \/>\nx + y = 27<br \/>\ny = x + 3<\/p>\n<p>Answer:<br \/>\nThe solution is (12, 15).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are x + y = 27, y = x + 3<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49538\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-14.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 14\" width=\"536\" height=\"533\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-14.jpg 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-14-300x298.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-14-150x150.jpg 150w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><br \/>\nThe lines intersect at (12, 15)<br \/>\nSo, the solution is (12, 15).<\/p>\n<p>Question 13.<br \/>\ny &#8211; x = 17<br \/>\ny = 4x + 2<\/p>\n<p>Answer:<br \/>\nThe solution is (5, 22)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y &#8211; x = 17, y = 4x + 2<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49539\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-15.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 15\" width=\"522\" height=\"521\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-15.jpg 522w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-15-300x300.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-15-150x150.jpg 150w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><br \/>\nThe lines intersect at (5, 22)<br \/>\nSo, the solution is (5, 22)<\/p>\n<p>Question 14.<br \/>\nx &#8211; y = 7<br \/>\n0.5x + y =5<\/p>\n<p>Answer:<br \/>\nThe solution is (8, 1).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are x &#8211; y = 7, 0.5x + y =5<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49540\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-16.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 16\" width=\"530\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-16.jpg 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-16-300x295.jpg 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><br \/>\nThe lines intersect at (8, 1)<br \/>\nSo, the solution is (8, 1)<\/p>\n<p><strong>USING A GRAPHING CALCULATOR<\/strong><br \/>\n<strong>Use a graphing calculator to solve the system.<\/strong><\/p>\n<p>Question 15.<br \/>\n2.2x + y = 12.5<br \/>\n1.4x &#8211; 4y =1<\/p>\n<p>Answer:<br \/>\nThe solution is (5, 1.5).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are 2.2x + y = 12.5, 1.4x &#8211; 4y = 1<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49542\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-17.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 17\" width=\"525\" height=\"527\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-17.jpg 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-17-300x300.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-17-150x150.jpg 150w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><br \/>\nThe lines intersect at (5, 1.5)<br \/>\nSo, the solution is (5, 1.5)<\/p>\n<p>Question 16.<br \/>\n2.1x + 4.2y = 14.7<br \/>\n-5.7x &#8211; 1.9y = -11.4<\/p>\n<p>Answer:<br \/>\nThe solution is (1, 3)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are 2.1x + 4.2y = 14.7, -5.7x &#8211; 1.9y = -11.4<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49544\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-18.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 18\" width=\"535\" height=\"532\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-18.jpg 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-18-300x298.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-18-150x150.jpg 150w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><br \/>\nThe lines intersect at (1, 3)<br \/>\nSo, the solution is (1, 3)<\/p>\n<p>Question 17.<br \/>\n-1.1x &#8211; 5.5y = -4.4<br \/>\n0.8x &#8211; 3.2y = -11.2<\/p>\n<p>Answer:<br \/>\nThe solution is (-6, 2)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are -1.1x &#8211; 5.5y = -4.4, 0.8x &#8211; 3.2y = -11.2<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49545\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-19.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 19\" width=\"536\" height=\"534\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-19.jpg 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-19-300x300.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-19-150x150.jpg 150w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><br \/>\nThe lines intersect at (-6, 2)<br \/>\nSo, the solution is (-6, 2)<\/p>\n<p>Question 18.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend solves the system of linear equations below. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32563\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-23.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 23\" width=\"217\" height=\"64\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32564\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-24.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 24\" width=\"301\" height=\"191\" \/><\/p>\n<p>Answer:<br \/>\nCorrect.<\/p>\n<p>Explanation:<br \/>\nThe given system of equations are y = 0.5x + 1, y = &#8211; + 7<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-34.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 34\" width=\"678\" height=\"678\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-34.jpg 678w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-34-300x300.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-34-150x150.jpg 150w\" sizes=\"(max-width: 678px) 100vw, 678px\" \/><br \/>\nThe point of intersection is (4, 3)<br \/>\nSo, the solution is (4, 3)<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject? Use a system of linear equations to justify your answer.<\/p>\n<p>Answer:<br \/>\n26 math and 16 science problems.<\/p>\n<p>Explanation:<br \/>\nWrite the system of equations where m and s are the number of math and science problems<br \/>\nm + s = 42 &#8212;- (1)<br \/>\nm = 10 + s &#8212;- (2)<br \/>\nSubstitute equation (2) in equation (1)<br \/>\n10 + s + s = 42<br \/>\n10 + 2s = 42<br \/>\n2s = 42 &#8211; 10<br \/>\n2s = 32<br \/>\ns = 32\/2<br \/>\ns = 16<br \/>\nPut s = 16 in equation (2)<br \/>\nm = 10 + 16<br \/>\nm = 26<br \/>\nSo, 26 math and 16 science problems.<\/p>\n<p>Question 20.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA generator contains 60 gallons of fuel and uses 2.5 gallons per hour. A more efficient power generator contains 40 gallons of fuel and uses 1.5 gallons per hour. After how many hours do the generators have the same amount of fuel? Which generator runs longer? Justify your answers.<\/p>\n<p>Answer:<br \/>\nAfter 20 hours both generators will be having an equal amount of fuel. The generator has 40 gallons of fuel that will run for a longer time.<\/p>\n<p>Explanation:<br \/>\nA generator contains 60 gallons of fuel and uses 2.5 gallons per hour. A more efficient power generator contains 40 gallons of fuel and uses 1.5 gallons per hour<br \/>\nLet&#8217;s assume that after x hours, both generate will have an equal amount of fuel<br \/>\nThus, fuel consumed by the first generator will be 2.5x gallons and for the more efficient generator will be 1.5x gallons<br \/>\nFuel left in the less efficient generator will be (60 &#8211; 2.5x) gallons. Fuel left in a more efficient generator will be (40 &#8211; 1.5x) gallons.<br \/>\n60 &#8211; 2.5x = 40 &#8211; 1.5x<br \/>\n-2.5x + 1.5x = 40 &#8211; 60<br \/>\n-x = -20<br \/>\nx = 20<br \/>\nThus, fuel left in each generator will be 60 &#8211; 2.5 * 20 = 10 gallons<br \/>\nNow lets find which generator will run longer.<br \/>\nThe number of hours less efficient generator would run is equal to 60\/2.5 = 24 hours<br \/>\nThe number of hours more efficient generator would run is equal to 40\/1.5 = 26.66 hours<br \/>\nHence, After 20 hours both generators will be having an equal amount of fuel.<br \/>\nThe generator has 40 gallons of fuel that will run for a longer time.<\/p>\n<p>Question 21.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou and your friend are in a canoe race. Your friend is a half-mile in front of you and paddling 3 miles per hour. You are paddling 3.4 miles per hour.<br \/>\na. You are 8.5 miles from the \ufb01nish line. How long will it take you to catch up with your friend? your friend<br \/>\nb. You both maintain your paddling rates for the remainder of the race. How far ahead of your friend will you be when you cross the \ufb01nish line?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32566\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-25.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 25\" width=\"184\" height=\"171\" \/><\/p>\n<p>Answer:<br \/>\na. It takes 1 hour 25 minutes for you to catch up to your friend.<br \/>\nb. You 0.5 miles ahead of your friend when you finish the race.<\/p>\n<p>Explanation:<br \/>\na. Let d be the distance traveled by your friend, h=then you have to travel d + 0.5 to catch up since you are currently 0.5 miles behind your friends.<br \/>\ndistance = rate * time<br \/>\nyou is d + 0.5 = 3.4t<br \/>\na friend is d = 3t<br \/>\nSubstitute the equation for your friend into the equation for y to solve d<br \/>\n3t + 0.5 = 3.4t<br \/>\n0.5 = 3.4t &#8211; 3t<br \/>\n0.4t = 0.5<br \/>\nt = 0.5\/0.4<br \/>\nt = 1.25<br \/>\nb. Time it takes you to complete the race<br \/>\n8.5 = 3.4t<br \/>\nt = 8.5\/3.4<br \/>\nt = 2.5<br \/>\nDistance traveled by a friend in that time 3(2.5) = 7.5<br \/>\nYour friend started 8 miles from the finishing line so you will be 8 &#8211; 7.5 = 0.5 miles ahead of your friend when you finish the race.<\/p>\n<p><strong>OPEN-ENDED<\/strong><br \/>\n<strong>Write a system of linear equations that \ufb01ts the description. Use a graph to justify your answer.<\/strong><\/p>\n<p>Question 22.<br \/>\nThe solution of the system is a point on the line y = -9x + 1.<\/p>\n<p>Answer:<br \/>\nThe equations have infinitely many solutions.<\/p>\n<p>Explanation:<br \/>\nThe given equation is y = -9x + 1<br \/>\nMultiply both sides by 2<br \/>\n2y = 2(-9x + 1)<br \/>\n2y = -18x + 2<br \/>\nDraw a graph for the system of equations y = -9x + 1, 2y = -18x + 2<br \/>\nThe equations have infinitely many solutions.<\/p>\n<p>Question 23.<br \/>\nThe solution of the system is (3, -1).<\/p>\n<p>Answer:<br \/>\nm = -1\/3<\/p>\n<p>Explanation:<br \/>\nThe slope intercept form is y = mx + c<br \/>\n-1 = 3m<br \/>\nm = -1\/3<\/p>\n<p>Question 24.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA graph of a system of two linear equations is shown. Write the system of linear equations represented by the graph. What is the solution to the system?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32565\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-25.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 25.1\" width=\"179\" height=\"156\" \/><\/p>\n<p>Answer:<br \/>\nThe systems of linear equations are y = -x + 2, y = 2x &#8211; 1<br \/>\nThe solution is (1, 1)<\/p>\n<p>Explanation:<br \/>\nfor line 1,<br \/>\nx\u2081 = 0, y\u2081 = 2, x\u2082 = 2, y\u2082 = 0<br \/>\nSlope m = (y\u2082 &#8211; y\u2081)\/(x\u2082 &#8211; x\u2081)<br \/>\n= (0 &#8211; 2)\/(2 &#8211; 0)<br \/>\n= -2\/2 = -1<br \/>\nSlope intercept form of a line is y = mx + b<br \/>\nThe line passes through (0, 2)<br \/>\n2 = 0(x) + b<br \/>\nb = 2<br \/>\ny = -1(x) + 2<br \/>\ny = -x + 2<br \/>\nFor line 2<br \/>\nx\u2081 = 2, y\u2081 = 3, x\u2082 = 0, y\u2082 = -1<br \/>\nSlope m = (-1 &#8211; 3)\/(0 &#8211; 2)<br \/>\n= -4\/-2<br \/>\n= 2<br \/>\ny = 2x + b<br \/>\nThe line passes through (0, -1)<br \/>\n-1 = 2(0) + b<br \/>\nn = -1<br \/>\nThe slope intercept form of a line is y = 2x &#8211; 1<br \/>\nSo, the systems of linear equations are y = -x + 2, y = 2x &#8211; 1<br \/>\nThe point of intersection in the graph is (1, 1)<\/p>\n<p>Question 25.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nYour friend is trying to grow her hair as long as her cousin\u2019s hair. The table shows their hair lengths (in inches) in different months.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32568\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-26.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 26\" width=\"248\" height=\"119\" \/><br \/>\na. Write a system of linear equations that represents this situation. Let x = 1 represent January.<br \/>\nb. Will your friend\u2019s hair ever be as long as her cousin\u2019s hair? If so, in what month?<\/p>\n<p>Answer:<br \/>\na. The equation of the line for a friend&#8217;s hair is y = 1\/2 x + 5\/2, the equation of the line for a friend&#8217;s cousin hair is y =2\/5x + 29\/5<br \/>\nb. After 33 months length of hair of both girls would be the same.<\/p>\n<p>Explanation:<br \/>\na. The length of hair is represented by y coordinate and month is represented as x coordinate<br \/>\nThe slope formula when we know two points is m = (y\u2082 &#8211; y\u2081)\/(x\u2082 &#8211; x\u2081)<br \/>\nx\u2081 = 3, y\u2081 = 4, x\u2082 = 8, y\u2082 = 6.5<br \/>\nm = (6.5 &#8211; 4)\/(8 -3)<br \/>\n= 2.5\/5<br \/>\nm = 1\/2<br \/>\nThe slope form of a line is (y &#8211; y\u2081) = m(x &#8211; x\u2081)<br \/>\ny &#8211; 4 = 1\/2 (x &#8211; 3)<br \/>\n2(y &#8211; 4) = (x &#8211; 3)<br \/>\n2y &#8211; 8 = x &#8211; 3<br \/>\n2y = x &#8211; 3 + 8<br \/>\n2y = x + 5<br \/>\ny = 1\/2 x + 5\/2<br \/>\nHence, the equation of line for friend&#8217;s hair is y = 1\/2 x + 5\/2<br \/>\nEquations of line for friend&#8217;s cousin hair<br \/>\nx\u2081 = 3, y\u2081 = 7, x\u2082 = 8, y\u2082 = 9<br \/>\nm = (y\u2082 &#8211; y\u2081)\/(x\u2082 &#8211; x\u2081)<br \/>\n= (9 &#8211; 7)\/(8 &#8211; 3)<br \/>\n= 2\/5<br \/>\nNow to find the equation of line for friends cousin hair<br \/>\n(y &#8211; y\u2081) = m(x &#8211; x\u2081)<br \/>\n(y &#8211; 7) = 2\/5 (x &#8211; 3)<br \/>\n5(y &#8211; 7) = 2(x &#8211; 3)<br \/>\n5y &#8211; 35 = 2x &#8211; 6<br \/>\n5y = 2x &#8211; 6 + 35<br \/>\n5y = 2x + 29<br \/>\ny = 2\/5x + 29\/5<br \/>\nHence, the equation of line for friend&#8217;s cousin hair is y =2\/5x + 29\/5<br \/>\nb.<br \/>\n2\/5x x + 29\/5 = 1\/2 x + 5\/2<br \/>\n2\/5 x &#8211; 1\/2x =5\/1 &#8211; 29\/5<br \/>\n(4x &#8211; 5x)\/10 = (25 &#8211; 58)\/10<br \/>\n-x\/10 = -33\/10<br \/>\nx = 33<br \/>\nHence, after 33 months length of hair of both girls would be same.<\/p>\n<p>Question 26.<br \/>\n<strong>REASONING<\/strong><br \/>\nIs it possible for a system of two linear equations to have multiple solutions? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nNo, it is not possible for a system of two linear equations to have multiple solutions. Because the system of linear equations is the straight lines and those lines intersect at only one point.<\/p>\n<p>Question 27.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nThe length of a rectangle is 8 feet more than its width. The perimeter of the rectangle is 72 feet. Find the width of the rectangle.<\/p>\n<p>Answer:<br \/>\nThe width of the rectangle is 14 ft.<\/p>\n<p>Explanation:<br \/>\nLet us say rectangle length is l, its width is l &#8211; 8<br \/>\nRectangle perimeter = 2(l + b)<br \/>\n72 = 2(l + l &#8211; 8)<br \/>\n72\/2 = 2l &#8211; 8<br \/>\n36 = 2l &#8211; 8<br \/>\n2l = 36 + 8<br \/>\n2l = 44<br \/>\nl = 44\/2<br \/>\nl = 22<br \/>\nrectangle width is 22 &#8211; 8 = 14 ft<\/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>EXPLORATION 1<\/strong><br \/>\n<strong>Work with a partner.<\/strong><br \/>\na. Find the value of each symbol in the systems below. Compare your solution methods with other pairs of students.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32567\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-26.1.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 26.1\" width=\"334\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-26.1.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-26.1-300x141.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><br \/>\nb. Use a method similar to your method in part(a) to solve the system below. Then explain how to solve a system of linear equations in two variables algebraically.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32569\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-27.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 27\" width=\"238\" height=\"62\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32570\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-28.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 28\" width=\"159\" height=\"174\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><br \/>\n<strong>Writing and Solving Systems of Equations<\/strong><br \/>\n<strong>Work with a partner. Roll two number cubes that are different colors. Then write the ordered pair shown by the number cubes.<\/strong><br \/>\na. Write a system of linear equations that has your ordered pair as its solution. Explain how you found your system.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32571\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-29.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 29\" width=\"302\" height=\"201\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-29.png 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-29-300x200.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><br \/>\nb. Exchange systems with another pair of students. Use a method from Exploration 1 to solve the system.<\/p>\n<p><strong>5.2 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the system by substitution. Check your solution.<\/strong><\/p>\n<p>Question 1.<br \/>\ny = 2x + 3<br \/>\ny = 5x<\/p>\n<p>Answer:<br \/>\nThe solution is (1, 1)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = 2x + 3 &#8212;- (i)<br \/>\ny = 5x &#8212;&#8211; (ii)<br \/>\nSubstitute equation (ii) in equation (i)<br \/>\n5x = 2x + 3<br \/>\n5x &#8211; 2x = 3<br \/>\n3x = 3<br \/>\nx = 3\/3<br \/>\nx = 1<br \/>\nSubstitute x = 1 in equation (ii)<br \/>\ny = 5(1)<br \/>\ny = 1<br \/>\nSo, the solution is (1, 1)<\/p>\n<p>Question 2.<br \/>\n4x + 2y = 0<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 5<\/p>\n<p>Answer:<br \/>\nThe solution is (0, -5)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n4x + 2y = 0 &#8212;&#8211; (i)<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 5 &#8212;&#8211; (ii)<br \/>\nSubstitute equation (ii) in equation (i)<br \/>\n4x + 2(1\/2 x) = 0<br \/>\n4x + x = 0<br \/>\n5x = 0<br \/>\nx = 0<br \/>\nputting x = 0 in equation (ii)<br \/>\ny = 1\/2 (0) &#8211; 5<br \/>\ny = -5<br \/>\nSo, the solution is (0, -5)<\/p>\n<p>Question 3.<br \/>\nx = 5y + 3<br \/>\n2x + 4y = -1<\/p>\n<p>Answer:<br \/>\nThe solution is (1\/2, -1\/2)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\nx = 5y + 3 &#8212;- (i)<br \/>\n2x + 4y = -1 &#8212;- (ii)<br \/>\nSubstitute equation (i) in equation (ii)<br \/>\n2(5y + 3) + 4y = -1<br \/>\n10y + 6 + 4y = -1<br \/>\n14y = -1 &#8211; 6<br \/>\n14y = -7<br \/>\ny = -7\/14<br \/>\ny = -1\/2<br \/>\nPut y = -1\/2 in equation (i)<br \/>\nx = 5(-1\/2) + 3<br \/>\n= -5\/2 + 3<br \/>\n= 1\/2<br \/>\nSo, the solution is (1\/2, -1\/2)<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the system. Explain your choice of method.<\/strong><\/p>\n<p>Question 4.<br \/>\ny = -3x + 2<br \/>\ny = 2<\/p>\n<p>Answer:<br \/>\nThe solution set is (0, 2)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = -3x + 2 &#8212;- (1)<br \/>\ny = 2 &#8212;- (2)<br \/>\nsubstitute equation (2) in (1)<br \/>\n2 = -3x + 2<br \/>\n2 &#8211; 2 = -3x<br \/>\n-3x = 0<br \/>\nx = 0<br \/>\nSo, the solution set is (0, 2)<\/p>\n<p>Question 5.<br \/>\n4y = x<br \/>\nx + 4y = -8<\/p>\n<p>Answer:<br \/>\nT4y = x<br \/>\nx + 4y = -8<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n4y = x &#8212;&#8211; (i)<br \/>\nx + 4y = -8 &#8212;&#8211; (ii)<br \/>\nSubstitute x = 4y in equation (ii)<br \/>\n4y + 4y = 8<br \/>\n8y = 8<br \/>\ny = 1<br \/>\nPut y = 1 in equation (i)<br \/>\n4(1) = x<br \/>\nx = 4<br \/>\nSo, the solution set is (4, 1)<\/p>\n<p>Question 6.<br \/>\n2x + 2y = 1<br \/>\n-x + 2y = -3<\/p>\n<p>Answer:<br \/>\nThe solution set is (4\/3, -5\/6)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n2x + 2y = 1 &#8212;- (i)<br \/>\n-x + 2y = -3<br \/>\n2y + 3 = x &#8212;- (ii)<br \/>\nSubstitute equation (ii) in equation (i)<br \/>\n2(2y + 3) + 2y = 1<br \/>\n4y + 6 + 2y = 1<br \/>\n6y + 6 = 1<br \/>\n6y = 1 &#8211; 6<br \/>\n6y = -5<br \/>\ny = -5\/6<br \/>\nPut y = -5\/6 in equation (ii)<br \/>\n2(-5\/6) + 3 = x<br \/>\nx = -5\/3 +3<br \/>\nx = 4\/3<br \/>\nSo, the solution set is (4\/3, -5\/6)<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\n<strong>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/strong><\/p>\n<p>Question 7.<br \/>\n<strong>REASONING<\/strong><br \/>\nDoes solving a system of linear equations by graphing give the same solution as solving by substitution? Explain.<\/p>\n<p>Answer:<br \/>\nYes.<\/p>\n<p><strong>SOLVING A SYSTEM OF LINEAR EQUATIONS<\/strong><br \/>\n<strong>Solve the system by substitution. Check your solution.<\/strong><\/p>\n<p>Question 8.<br \/>\ny = x &#8211; 8<br \/>\ny = 2x &#8211; 14<\/p>\n<p>Answer:<br \/>\nThe solution set is (6, -2)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = x &#8211; 8 &#8212;- (i)<br \/>\ny = 2x &#8211; 14 &#8212;- (ii)<br \/>\nSubstitute equation (i) in (ii)<br \/>\nx &#8211; 8 = 2x &#8211; 14<br \/>\n-8 + 14 = 2x &#8211; x<br \/>\nx = 6<br \/>\nPutting x = 6 in equation (i)<br \/>\ny = 6 &#8211; 8<br \/>\ny = -2<br \/>\nSubstitute x = 6, y = -2 in equation (i)<br \/>\n-2 = 6 &#8211; 8<br \/>\nSo, the solution set is (6, -2)<\/p>\n<p>Question 9.<br \/>\nx = 2y + 2<br \/>\n2x &#8211; 5y = 1<\/p>\n<p>Answer:<br \/>\nThe solution set is (8, 3)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\nx = 2y + 2 &#8212;- (i)<br \/>\n2x &#8211; 5y = 1 &#8212;- (ii)<br \/>\nSubstituting equation (i) in (ii)<br \/>\n2(2y + 2) &#8211; 5y = 1<br \/>\n4y + 4 &#8211; 5y = 1<br \/>\n4 &#8211; 1 = y<br \/>\ny = 3<br \/>\nPut y = 3 in equation (i)<br \/>\nx = 2(3) + 2<br \/>\nx = 8<br \/>\nSubstitute x = 8, y = 3 in 2x &#8211; 5y = 1<br \/>\n2(8) &#8211; 5(3) = 16 &#8211; 15 = 1<br \/>\nSo, the solution set is (8, 3)<\/p>\n<p>Question 10.<br \/>\nx &#8211; 5y = 1<br \/>\n-2x + 9y = -1<\/p>\n<p>Answer:<br \/>\nThe solution is (-4, -1)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\nx &#8211; 5y = 1<br \/>\nx = 1 + 5y &#8212;&#8211; (i)<br \/>\n-2x + 9y = -1 &#8212;- (ii)<br \/>\nSubstitute equation (i) in (ii)<br \/>\n-2(1 + 5y) + 9y = -1<br \/>\n-2 &#8211; 10y + 9y = -1<br \/>\n-2 &#8211; y = -1<br \/>\ny = -2 + 1<br \/>\ny = -1<br \/>\nPut y = -1 in (i)<br \/>\nx = 1 + 5(-1)<br \/>\nx = 1 &#8211; 5<br \/>\nx = -4<br \/>\nPut x = -4, y = -1 in (ii)<br \/>\n-2(-4) + 9(-1) = 8 &#8211; 9 = -1<br \/>\nSo, the solution is (-4, -1)<\/p>\n<p><strong>CHOOSING A SOLUTION METHOD<\/strong><\/p>\n<p><strong>Solve the system. Explain your choice of method.<\/strong><\/p>\n<p>Question 11.<br \/>\ny = -x + 3<br \/>\ny = 2x<\/p>\n<p>Answer:<br \/>\nThe solution set is (1, 2).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = -x + 3<br \/>\ny = 2x<br \/>\nEquating both equations<br \/>\n-x + 3 = 2x<br \/>\n3 = 2x + x<br \/>\n3x = 3<br \/>\nx = 1<br \/>\nSubstitute x = 1 in y = 2x<br \/>\ny = 2(1)<br \/>\ny = 2<br \/>\nSo, the solution set is (1, 2).<\/p>\n<p>Question 12.<br \/>\n0.5x + y = 2<br \/>\n0.5x = 1 + y<\/p>\n<p>Answer:<br \/>\nThe solution set is (3, 1\/2).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n0.5x + y = 2 &#8212;&#8212; (i)<br \/>\n0.5x = 1 + y<br \/>\nx = 1\/0.5 + y\/0.5<br \/>\nx = 2 + 2y &#8212;- (ii)<br \/>\nSubstitute equation (ii) in (i)<br \/>\n0.5(2 + 2y) + y = 2<br \/>\n1 + y + y = 2<br \/>\n2y + 1 = 2<br \/>\n2y = 2 &#8211; 1<br \/>\n2y = 1<br \/>\ny = 1\/2<br \/>\nPut y = 1\/2 in equation (i)<br \/>\n0.5x + 1\/2 = 2<br \/>\n0.5x = 2 &#8211; 0.5<br \/>\n0.5x = 1.5<br \/>\nx = 1.5\/0.5<br \/>\nx = 3<br \/>\nSo the solution set is (3, 1\/2).<\/p>\n<p>Question 13.<br \/>\nx = 5y<br \/>\ny = 22 &#8211; 2x<\/p>\n<p>Answer:<br \/>\nThe solution set is (10, 2)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\nx = 5y &#8212;- (i)<br \/>\ny = 22 &#8211; 2x &#8212;&#8211; (ii)<br \/>\nSubstitute x = 5y in equation (ii)<br \/>\ny = 22 &#8211; 2(5y)<br \/>\ny = 22 &#8211; 10y<br \/>\ny + 10y = 22<br \/>\n11y = 22<br \/>\ny = 2<br \/>\nPut y = 2 in x = 5y<br \/>\nx = 5(2)<br \/>\nx = 10<br \/>\nSo, the solution set is (10, 2)<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 14.<br \/>\nTo stock your school store, you buy a total of 25 sweatshirts and hats for $172.50. You pay $8.00 per sweatshirt and $2.50 per hat. How many of each item do you buy?<\/p>\n<p>Answer:<br \/>\nThe number of sweatshirts you buy would be 20 and the hat you buy would be 5.<\/p>\n<p>Explanation:<br \/>\nLet&#8217;s assume the number of sweatshirts bought be x, while the number of hats will be 25 &#8211; x<br \/>\nThus, cost to buy sweatshirts is 8 * x = 8x, and for hats will be 2.5 * (25 &#8211; x) = 62.50 &#8211; 2.50x<br \/>\nTherefore, total cost is 8x + 62.50 &#8211; 2.5x which is equal to 172.50<br \/>\n8x + 62.50 &#8211; 2.5x = 172.50<br \/>\n5.5x = 172.50 &#8211; 62.50<br \/>\n5.5x = 110<br \/>\nx = 110\/5.5<br \/>\nx = 20<br \/>\nHence, the cost of buying sweatshirts will be $20 * 8 = $160 and the cost to buy hats will be (25 &#8211; 20)2.50 = 12.5<br \/>\nThe number of sweatshirts you buy would be 20 and the hat you buy would be (25 &#8211; 20) = 5<\/p>\n<p>Question 15.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe length of a volleyball court is twice its width. The perimeter of the court is 180 feet. Find the area of the volleyball court. Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe area of the rectangle will be 1800 sq ft.<\/p>\n<p>Explanation:<br \/>\nThe perimeter of the volleyball court is 180 feet. The length of the court is twice its width<br \/>\nLet us take the length and width of the court be 2x, x<br \/>\nPerimeter = 2(l + b)<br \/>\nAs per the question<br \/>\n2(l + b) = 180<br \/>\n2x + x = 90<br \/>\n3x = 90<br \/>\nx = 90\/3<br \/>\nx = 30<br \/>\nThus, the length of court is 2 . 30 = 60 and width is 30 ft<br \/>\nArea = length * width<br \/>\n= 60 * 30<br \/>\n= 1800<br \/>\nHence, the area of the rectangle will be 1800 sq ft.<\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_by_Substitution_Homework_&amp;_Practice_5.2\"><\/a>Solving Systems of Linear Equations by Substitution Homework &amp; Practice 5.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Solve the system by graphing.<\/strong><\/p>\n<p>Question 1.<br \/>\ny = 2x &#8211; 3<br \/>\ny = -x + 9<\/p>\n<p>Answer:<br \/>\nThe solution is (4, 5)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = 2x &#8211; 3, y = -x + 9<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49546\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-20.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 20\" width=\"548\" height=\"540\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-20.jpg 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-20-300x296.jpg 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><br \/>\nThe lines intersect at (4, 5)<br \/>\nSo, the solution is (4, 5)<\/p>\n<p>Question 2.<br \/>\n6x + y = -2<br \/>\ny = -3x + 1<\/p>\n<p>Answer:<br \/>\nThe solution is (-1, 4)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are 6x + y = -2, y = -3x + 1<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49547\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-21.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 21\" width=\"526\" height=\"533\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-21.jpg 526w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-21-296x300.jpg 296w\" sizes=\"(max-width: 526px) 100vw, 526px\" \/><br \/>\nThe lines intersect at (-1, 4)<br \/>\nSo, the solution is (-1, 4)<\/p>\n<p>Question 3.<br \/>\n4x + 2y = 2<br \/>\n3x = 4 &#8211; y<\/p>\n<p>Answer:<br \/>\nThe solution is (3, -5).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are 4x + 2y = 2, 3x = 4 &#8211; y<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49549\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-22.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 22\" width=\"532\" height=\"534\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-22.jpg 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-22-300x300.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-22-150x150.jpg 150w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><br \/>\nThe lines intersect at (3, -5)<br \/>\nSo, the solution is (3, -5)<\/p>\n<p>Question 4.<br \/>\nUse the figure to find the measure of \u22202<br \/>\nA. 17\u00b0<br \/>\nB. 73\u00b0<br \/>\nC. 83\u00b0<br \/>\nD. 107\u00b0<\/p>\n<p>Answer:<br \/>\nB. 73\u00b0<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n\u22201 = 107 degrees<br \/>\n\u22201 + \u22202 = 180<br \/>\n107 + \u22202 = 180<br \/>\n\u22202 = 180 &#8211; 107<br \/>\n= 73 degrees<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><br \/>\n<strong>SOLVING A SYSTEM ALGEBRAICALLY<\/strong><br \/>\n<strong>Find the value of each symbol in the system.<\/strong> (See Exploration 1, p. 205.)<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32572\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-30.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 30\" width=\"228\" height=\"76\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32573\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-31.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 31\" width=\"242\" height=\"80\" \/><\/p>\n<p><strong>SOLVING A SYSTEM OF LINEAR EQUATIONS<\/strong><br \/>\n<strong>Solve the system by substitution. Check your solution.<\/strong><\/p>\n<p>Question 7.<br \/>\ny = x &#8211; 4<br \/>\ny = 4x &#8211; 10<\/p>\n<p>Answer:<br \/>\nThe solution set is (2, -2).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = x &#8211; 4 &#8212;- (i)<br \/>\ny = 4x &#8211; 10 &#8212;&#8211; (ii)<br \/>\nSubstitute (ii) in (i)<br \/>\n4x &#8211; 10 = x &#8211; 4<br \/>\n4x &#8211; x = -4 + 10<br \/>\n3x = 6<br \/>\nx = 2<br \/>\nPut x = 2 in (i)<br \/>\ny = 2 &#8211; 4<br \/>\ny = -2<br \/>\nSubstitute x = 2, y = -2 in equation (ii)<br \/>\n-2 = 4(2) &#8211; 10<br \/>\n= 8 &#8211; 10<br \/>\nSo, the solution set is (2, -2).<\/p>\n<p>Question 8.<br \/>\ny = 2x + 5<br \/>\ny = 3x &#8211; 1<\/p>\n<p>Answer:<br \/>\nThe solution set is (6, 17).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = 2x + 5 &#8212;&#8211; (i)<br \/>\ny = 3x &#8211; 1 &#8212;&#8212; (ii)<br \/>\nSubstitute (ii) in (i)<br \/>\n3x &#8211; 1 = 2x + 5<br \/>\n3x &#8211; 2x = 5 + 1<br \/>\nx = 6<br \/>\nSubstitute x = 6 in (i)<br \/>\ny = 2(6) + 5<br \/>\ny = 12 + 5<br \/>\ny = 17<br \/>\nPut x = 6, y = 17 in (ii)<br \/>\n17 = 3(6) &#8211; 1<br \/>\n= 18 &#8211; 1<br \/>\nSo, the solution set is (6, 17)<\/p>\n<p>Question 9.<br \/>\nx = 2y + 7<br \/>\n3x &#8211; 2y = 3<\/p>\n<p>Answer:<br \/>\nThe solution set is (-2, -9\/2).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\nx = 2y + 7 &#8212;&#8211; (i)<br \/>\n3x &#8211; 2y = 3\u00a0 &#8212;&#8211; (ii)<br \/>\nSubstitute (i) in (ii)<br \/>\n3(2y + 7) &#8211; 2y = 3<br \/>\n6y + 21 &#8211; 2y = 3<br \/>\n4y = 3 &#8211; 21<br \/>\n4y = -18<br \/>\ny = -9\/2<br \/>\nSubstitute y = -9\/2 in (i)<br \/>\nx = 2(-9\/2) + 7<br \/>\nx = -9 + 7<br \/>\nx = -2<br \/>\nPut x = -2, y = -9\/2 in (ii)<br \/>\n3(-2) &#8211; 2(-9\/2) = -6 + 9 = 3<br \/>\nSo, the solution set is (-2, -9\/2)<\/p>\n<p>Question 10.<br \/>\n4x &#8211; 2y =14<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 1<\/p>\n<p>Answer:<br \/>\nThe solution set is (4, 1)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n4x &#8211; 2y =14 &#8212;&#8211; (i)<br \/>\ny = \\(\\frac{1}{2}\\)x &#8211; 1 &#8212;&#8211; (ii)<br \/>\nSubstitute equation (i) in (ii)<br \/>\n4x &#8211; 2(0.5x &#8211; 1) = 14<br \/>\n4x &#8211; x + 2 = 14<br \/>\n3x = 14 &#8211; 2<br \/>\n3x = 12<br \/>\nx = 4<br \/>\nSubstitute x = 4 in (i)<br \/>\n4(4) &#8211; 2y = 14<br \/>\n16 &#8211; 14 = 2y<br \/>\n2 = 2y<br \/>\ny = 1<br \/>\nPut x = 4, y = 1 in (ii)<br \/>\n1 = 1\/2 (4) &#8211; 1<br \/>\n= 2 &#8211; 1<br \/>\nSo, the solution set is (4, 1)<\/p>\n<p>Question 11.<br \/>\n2x = y &#8211; 10<br \/>\n2x + 7 = 2y<\/p>\n<p>Answer:<br \/>\nThe solution set is (-13\/2, -3)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n2x = y &#8211; 10<br \/>\ny = 2x + 10 &#8212;- (i)<br \/>\n2x + 7 = 2y &#8212;&#8212; (ii)<br \/>\nSubstitute (i) in (ii)<br \/>\n2x + 7 = 2(2x + 10)<br \/>\n2x + 7 = 4x + 20<br \/>\n4x &#8211; 2x = 7 &#8211; 20<br \/>\n2x = -13<br \/>\nx = -13\/2<br \/>\nSubstitute x = -13\/2 in (i)<br \/>\ny = 2(-13\/2) + 10<br \/>\n= -13 + 10<br \/>\n= -3<br \/>\nPut x = -13\/2, y = -3 in (ii)<br \/>\n2(-13\/2) + 7 = 2(-3)<br \/>\n-13 + 7 = -6<br \/>\nSo, the solution set is (-13\/2, -3)<\/p>\n<p>Question 12.<br \/>\n8x &#8211; \\(\\frac{1}{3}\\)y = 0<br \/>\n12x + 3 =y<\/p>\n<p>Answer:<br \/>\nThe solution set is (1\/4, 6).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n8x &#8211; \\(\\frac{1}{3}\\)y = 0 &#8212;&#8211; (i)<br \/>\n12x + 3 =y &#8212;&#8212; (ii)<br \/>\nSubstitute (ii) in (i)<br \/>\n8x &#8211; 1\/3(12x + 3) = 0<br \/>\n8x &#8211; 4x &#8211; 1 = 0<br \/>\n4x &#8211; 1 = 0<br \/>\n4x = 1<br \/>\nx = 1\/4<br \/>\nSubstitute x = 1\/4 in (ii)<br \/>\n12(1\/4) + 3 = y<br \/>\n3 + 3 = y<br \/>\ny = 6<br \/>\nPut x = 1\/4, y = 6 in (ii)<br \/>\n12(1\/4) + 3 = 3 + 3 = 6<br \/>\nSo, the solution set is (1\/4, 6).<\/p>\n<p>Question 16.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThere are a total of 64 students in a \ufb01lm making club and a yearbook club. The \ufb01lmmaking club has 14 more students than the yearbook club.<br \/>\na. Write a system of linear equations that represents this situation.<br \/>\nb. How many students are in the \ufb01lm making club? the yearbook club?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32574\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-32.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 32\" width=\"277\" height=\"198\" \/><\/p>\n<p>Answer:<br \/>\na. x + y = 64, x = y + 14<br \/>\nb. The number of students in the filmmaking club and yearbook club are 39 and 25 respectively.<\/p>\n<p>Explanation:<br \/>\na. Let us take the number of students in film making club to be x and the number of students in the yearbook club be y<br \/>\nx + y = 64 &#8212;- (i)<br \/>\nIt is given that the number of students in the filmmaking club is greater than students in the yearbook club by 14<br \/>\nSo, x = y + 14 &#8212;- (ii)<br \/>\nb. Put equation (ii) in (i)<br \/>\ny + 14 + y = 64<br \/>\n2y + 14 = 64<br \/>\n2y = 64 &#8211; 14<br \/>\n2y = 50<br \/>\ny = 25<br \/>\nSubstitute y = 25 in (i)<br \/>\nx + 25 = 64<br \/>\nx = 64 &#8211; 25<br \/>\nx = 39<br \/>\nHence, the number of students in filmmaking club and yearbook club are 39 and 25 respectively.<\/p>\n<p>Question 17.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA drama club earns $1040 from production by selling 64 adult tickets and 132 student tickets. An adult ticket costs twice as much as a student ticket.<br \/>\na. Write a system of linear equations that represents this situation.<br \/>\nb. What is the cost of each ticket?<\/p>\n<p>Answer:<br \/>\na. 64a + 132s = 1040, a = 2s<br \/>\nb. The price of a student ticket is $4, adult ticket is $8.<\/p>\n<p>Explanation:<br \/>\nWrite the system of equations that models the problem where a is the price of an adult ticket and s is the price of a student ticket<br \/>\n64a + 132s = 1040<br \/>\na = 2s<br \/>\nb. Substitute a = 2s in 64a + 132s = 1040<br \/>\n64(2s) + 132s = 1040<br \/>\n128s + 132s = 1040<br \/>\n260s = 1040<br \/>\ns = 1040\/260<br \/>\ns = $4 per student ticket<br \/>\na = 2(4) = $8 per adult ticket.<\/p>\n<p>Question 18.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite a system of linear equations that has the ordered pair (1, 6) as its solution.<\/p>\n<p>Answer:<br \/>\nThe system of linear equations that pass through (1, 6) is y &#8211; 6 = m(x &#8211; 1)<\/p>\n<p>Explanation:<br \/>\nWe know that the equation of a line that passes through a point is (y &#8211; y\u2081) = m(x &#8211; x\u2081)<br \/>\nThe line pass through (1,6 )<br \/>\nSo, y &#8211; 6 = m(x &#8211; 1)<br \/>\nWe can get system of linear equations by inserting different values of m in above equation<br \/>\nIf we put m = 1, then equation is y &#8211; 6 = 1(x &#8211; 1)<br \/>\ny &#8211; 6 = x &#8211; 1<br \/>\ny = x &#8211; 1 + 6<br \/>\ny = x + 5<br \/>\nHence, the system of linear equation is y &#8211; 6 = m(x &#8211; 1) that pass through (1, 6).<\/p>\n<p><strong>CHOOSING A SOLUTION METHOD<\/strong><br \/>\n<strong>Solve the system. Explain your choice of method.<\/strong><\/p>\n<p>Question 19.<br \/>\ny &#8211; x = 4<br \/>\nx + y = 6<\/p>\n<p>Answer:<br \/>\nThe solution set is (1, 5)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\ny &#8211; x = 4<br \/>\ny = 4 + x &#8212;&#8211; (i)<br \/>\nx + y = 6 &#8212;&#8211; (ii)<br \/>\nSubstitute (i) in (ii)<br \/>\nx + 4 + x = 6<br \/>\n2x + 4 = 6<br \/>\n2x = 6 &#8211; 4<br \/>\n2x = 2<br \/>\nx = 1<br \/>\nSubstitute x = 1 in (i)<br \/>\ny = 4 + 1<br \/>\ny = 5<br \/>\nSo, the solution set is (1, 5)<\/p>\n<p>Question 20.<br \/>\n0.5x + y = 4<br \/>\n0.5x &#8211; y =-1<\/p>\n<p>Answer:<br \/>\nThe solution set is (3, 2.5)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n0.5x + y = 4 &#8212;- (i)<br \/>\n0.5x &#8211; y =-1<br \/>\n0.5x + 1 = y &#8212;- (ii)<br \/>\nSubstitute (ii) in (i)<br \/>\n0.5x + 0.5x + 1 = 4<br \/>\nx + 1 = 4<br \/>\nx = 4 &#8211; 1<br \/>\nx = 3<br \/>\nSubstitute x = 3 in (ii)<br \/>\ny = 0.5(3) + 1<br \/>\n= 2.5<br \/>\nSo, the solution set is (3, 2.5)<\/p>\n<p>Question 21.<br \/>\ny = 2x + 5<br \/>\ny = -3x<\/p>\n<p>Answer:<br \/>\nThe solution set is (-1, 3)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\ny = 2x + 5 &#8212;- (i)<br \/>\ny = -3x &#8212;&#8211; (ii)<br \/>\nSubstitute (i) in (ii)<br \/>\n-3x = 2x + 5<br \/>\n-3x &#8211; 2x = 5<br \/>\n-5x = 5<br \/>\nx = -1<br \/>\nSubstitute x = -1 in (i)<br \/>\ny = 2(-1) + 5<br \/>\ny = -2 + 5<br \/>\ny = 3<br \/>\nSo, the solution set is (-1, 3)<\/p>\n<p>Question 22.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nA system consists of two different proportional relationships. What is the solution to the system? Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe solution is (0, 0).<\/p>\n<p>Explanation:<br \/>\nThe proportional relationships in the system of linear equations mean that there is no constant available in the equation.<br \/>\nTherefore, the lines will always pass through the origin (0, 0)<br \/>\nHence, the solution is (0, 0).<\/p>\n<p>Question 23.<br \/>\n<strong>GEOMETRY<\/strong><br \/>\nThe measure of the obtuse angle in the isosceles triangle is two and a half times the measure of one of the acute angles. Write and solve a system of linear equations to \ufb01nd the measure of each angle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32575\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-33.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 33\" width=\"191\" height=\"96\" \/><\/p>\n<p>Answer:<br \/>\nThe systems of linear equations are x + 2y = 180\u00b0, x = 2.5y<br \/>\nx = 100\u00b0, y = 40\u00b0<\/p>\n<p>Explanation:<br \/>\nIn an isosceles triangle, there are two angles that are the same and one that is different. We know there is one angle that is more than 90\u00b0 because that is the definition of an obtuse angle. We also know that the sum of all the angles of a triangle equals 180\u00b0.<br \/>\nLet&#8217;s put all this together and find the measures of the angles.<br \/>\nx + 2y = 180\u00b0<br \/>\nx = 2.5y<br \/>\nPut x = 2.5 y in x + 2y = 180\u00b0<br \/>\n2.5y + 2y = 180\u00b0<br \/>\n4.5y = 180<br \/>\ny = 180\/4.5<br \/>\ny = 40<br \/>\nPut y = 40 in x = 2.5y<br \/>\nx = 2.5(40)<br \/>\nx = 100<\/p>\n<p>Question 24.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nThe sum of the digits of a two-digit number is 8. When the digits are reversed, the number increases by 36. Find the original number.<\/p>\n<p>Answer:<br \/>\nThe original number is 26.<\/p>\n<p>Explanation:<br \/>\nLet the two-digit number be xy<br \/>\nThe sum of the digits of a two-digit number is 8<br \/>\nx + y = 8<br \/>\ny = 8 &#8211; x &#8212;- (i)<br \/>\nSo, the number is 10x + y<br \/>\nWhen the digits are reversed, the number increases by 36<br \/>\n10y + x = 36 + 10x + y<br \/>\n10y &#8211; y = 36 + 10x &#8211; x<br \/>\n9y = 36 + 9x<br \/>\nPut y = 8 &#8211; x<br \/>\n9(8 &#8211; x) = 36 + 9x<br \/>\n72 &#8211; 9x = 36 + 9x<br \/>\n72 &#8211; 36 = 18x<br \/>\n18x = 36<br \/>\nx = 36\/18<br \/>\nx = 2<br \/>\nPut x = 2 in equation (i)<br \/>\ny = 8 &#8211; 2<br \/>\ny = 6<br \/>\nSo, the original number is 26.<\/p>\n<p>Question 25.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA hospital employs a total of 77 nurses and doctors. The ratio of nurses to doctors is 9 : 2. How many nurses are employed at the hospital? How many doctors are employed at the hospital?<\/p>\n<p>Answer:<br \/>\nThere are 63 nurses, 14 doctors are employed at the hospital.<\/p>\n<p>Explanation:<br \/>\nLet x be the number of nurses and y be the number of doctors<br \/>\nA hospital employs a total of 77 nurses and doctors<br \/>\nx + y = 77 &#8212;- (i)<br \/>\nThe ratio of nurses to doctors is 9:2.<br \/>\nx\/y = 9\/2<br \/>\nx = 9\/2y<br \/>\nPut x = 9\/2y in (i)<br \/>\n9\/2 y + y = 77<br \/>\n11\/2 y = 77<br \/>\n11y = 77 * 2<br \/>\ny = 14<br \/>\nx = 9\/2 (14)<br \/>\ny = 63<br \/>\nSo, there are 63 nurses, 14 doctors are employed at the hospital.<\/p>\n<p>Question 26.<br \/>\n<strong>REPEATED REASONING<\/strong><br \/>\nA DJ has a total of 1075 dance, rock, and country songs on her system. The dance selection is three times the rock selection. The country selection has 105 more songs than the rock selection. How many songs on the system is dance? rock? country?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32576\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-34.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 34\" width=\"382\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-34.png 382w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-34-300x246.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><\/p>\n<p>Answer:<br \/>\n582 dance, 299 countries, and 194 ock songs on the system.<\/p>\n<p>Explanation:<br \/>\nLet d, r, c be the number of dance, rock and country songs<br \/>\nA DJ has a total of 1075 dance, rock, and country songs on her system<br \/>\nd + r + c = 1075 &#8212;- (i)<br \/>\nThe dance selection is three times the size of the rock selection<br \/>\nd = 3r &#8212;- (ii)<br \/>\nThe country selection has 105 more songs than the rock selection<br \/>\nc = 105 + r &#8212;&#8211; (iii)<br \/>\nPut (ii), (iii) in (i)<br \/>\n3r + r + 105 + r = 1075<br \/>\n5r = 1075 &#8211; 105<br \/>\n5r = 970<br \/>\nr = 194<br \/>\nd = 3(194) = 582<br \/>\nc = 105 + 194 = 299<br \/>\nSo, 582 dance, 299 country, and 194 ock songs on the system.<\/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>EXPLORATION 1<\/strong><br \/>\n<strong>Work with a partner. A student found the value of in the system using substitution as shown.<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32577\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-35.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 35\" width=\"435\" height=\"287\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-35.png 435w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-35-300x198.png 300w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><br \/>\na. Find another way to obtain the equation 4x = -4 from the original system. Does your method produce an equation in one variable for any system? Explain.<br \/>\nb. Can you use your method in part(a) to solve each system below? If so, solve the system. If not, replace one of the equations with an equivalent equation that allows you to use your method in part(a). Then solve the system.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32578\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-36.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 36\" width=\"609\" height=\"186\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-36.png 609w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-36-300x92.png 300w\" sizes=\"(max-width: 609px) 100vw, 609px\" \/><br \/>\nc. Compare your solution methods in part(b) with other pairs of students.<\/p>\n<p><strong>5.3 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the system by elimination. Check your solution.<\/strong><\/p>\n<p>Question 1.<br \/>\n2x &#8211; y = 9<br \/>\n4x + y =21<\/p>\n<p>Answer:<br \/>\nThe solution set is (5, 1).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n2x &#8211; y = 9 &#8212;- (i)<br \/>\n4x + y =21 &#8212;&#8211; (ii)<br \/>\nAdd both equations<br \/>\n2x &#8211; y + 4x + y = 9 + 21<br \/>\n6x = 30<br \/>\nx = 30\/6<br \/>\nx = 5<br \/>\nPut x = 5 in (i)<br \/>\n2(5) &#8211; y = 9<br \/>\n10 &#8211; y = 9<br \/>\n10 &#8211; 9 = y<br \/>\ny = 1<br \/>\nSubstitute x = 5, y = 1 in (ii)<br \/>\n4(5) + 1 = 20 + 1 = 21<br \/>\nSo, the solution set is (5, 1).<\/p>\n<p>Question 2.<br \/>\n-5x + 2y = 13<br \/>\n5x + y = -1<\/p>\n<p>Answer:<br \/>\nThe solution set is (-1, 4).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n-5x + 2y = 13 &#8212;&#8211; (i)<br \/>\n5x + y = -1 &#8212;&#8212; (ii)<br \/>\nAdd both equations<br \/>\n-5x + 2y + 5x + y = 13 &#8211; 1<br \/>\n3y = 12<br \/>\ny = 4<br \/>\nSubstitute y = 4 in (ii)<br \/>\n5x + 4 = -1<br \/>\n5x = -1 &#8211; 4<br \/>\n5x = -5<br \/>\nx = -1<br \/>\nSubstitute x = -1, y = 4 in (i)<br \/>\n-5(-1) + 2(4) = 5 + 8 = 13<br \/>\nSo, the solution set is (-1, 4).<\/p>\n<p>Question 3.<br \/>\n3x + 4y = -6<br \/>\n7x + 4y = -14<\/p>\n<p>Answer:<br \/>\nThe solution set is (-2, 0).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n3x + 4y = -6 &#8212;- (i)<br \/>\n7x + 4y = -14 &#8212;&#8211; (ii)<br \/>\nSubtract (ii) from (i)<br \/>\n3x + 4y &#8211; (7x + 4y) = -6 + 14<br \/>\n3x + 4y &#8211; 7x &#8211; 4y = 8<br \/>\n-4x = 8<br \/>\nx = -8\/4<br \/>\nx = -2<br \/>\nSubstitute x = -2 in (i)<br \/>\n3(-2) + 4y = -6<br \/>\n-6 + 4y = -6<br \/>\n4y = -6 + 6<br \/>\ny = 0<br \/>\nSubstitute x = -2, y = 0 in (ii)<br \/>\n7(-2) + 4(0) = -14<br \/>\nSo, the solution set is (-2, 0).<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the system by elimination. Check your solution.<\/strong><\/p>\n<p>Question 4.<br \/>\n3x + y = 11<br \/>\n6x + 3y = 24<\/p>\n<p>Answer:<br \/>\nThe solution set is (3, 2)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n3x + y = 11 &#8212;&#8212; (i)<br \/>\n6x + 3y = 24 &#8212;&#8212;- (ii)<br \/>\nDivide equation (ii) by 1\/3<br \/>\n1\/3(6x + 3y = 24)<br \/>\n2x + y = 8 &#8212;- (iii)<br \/>\nSubtract (iii) from (i)<br \/>\n3x + y &#8211; (2x + y) = 11 &#8211; 8<br \/>\n3x + y &#8211; 2x &#8211; y = 3<br \/>\nx = 3<br \/>\nPut x = 3 in (i)<br \/>\n3(3) + y = 11<br \/>\n9 + y = 11<br \/>\ny = 11 &#8211; 9<br \/>\ny = 2<br \/>\nSubstitute x = 3, y = 2 in (iii)<br \/>\n2(3) + 2 = 6 + 2 = 8<br \/>\nSo, the solution set is (3, 2)<\/p>\n<p>Question 5.<br \/>\n4x &#8211; 5y = -19<br \/>\n-x &#8211; 2y = 8<\/p>\n<p>Answer:<br \/>\nThe solution set is (-6, -1)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n4x &#8211; 5y = -19 &#8212;&#8211; (i)<br \/>\n-x &#8211; 2y = 8 &#8212;&#8212; (ii)<br \/>\nMultiply both sides of equation (ii) by 4<br \/>\n4(-x &#8211; 2y = 8)<br \/>\n-4x &#8211; 8y = 32 &#8212;- (iii)<br \/>\nAdd (i) &amp; (iii)<br \/>\n4x &#8211; 5y &#8211; 4x &#8211; 8y = -19 + 32<br \/>\n-13y = 13<br \/>\ny = -1<br \/>\nSubstitute y = -1 in (ii)<br \/>\n-x &#8211; 2(-1) = 8<br \/>\n-x + 2 = 8<br \/>\n-x = 8 &#8211; 2<br \/>\nx = -6<br \/>\nSubstitute x = -6, y = -1 in (ii)<br \/>\n-(-6) &#8211; 2(-1) = 6 + 2 = 8<br \/>\nSo, the solution set is (-6, -1)<\/p>\n<p>Question 6.<br \/>\n5y = 15 &#8211; 5x<br \/>\ny = -2x + 3<\/p>\n<p>Answer:<br \/>\nThe solution set is (0, 3)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n5y = 15 &#8211; 5x &#8212;&#8211; (i)<br \/>\ny = -2x + 3 &#8212;&#8211; (ii)<br \/>\nDivide equation (i) by 1\/5<br \/>\n1\/5(5y = 15 &#8211; 5x)<br \/>\ny = 3 &#8211; x &#8212;&#8211; (iii)<br \/>\nSubtract (iii) from (ii)<br \/>\ny &#8211; y = -2x + 3 &#8211; (3 &#8211; x)<br \/>\n0 = -2x + 3 &#8211; 3 + x<br \/>\n-x = 0<br \/>\nx = 0<br \/>\nSubstitute x = 0 in (iii)<br \/>\ny = 3 &#8211; 0<br \/>\ny = 3<br \/>\nSubstitute x = 0, y = 3 in (ii)<br \/>\n3 = -2(0) + 3<br \/>\nSo, the solution set is (0, 3)<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 7.<br \/>\nChange one word in Choice B so that it represents an efficient approach to solving the system.<\/p>\n<p>Answer:<br \/>\nMultiply equation (i) by -1 and subtract the equations.<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\nx &#8211; 2y = 6 &#8212;- (i)<br \/>\n-x + 4y = 6 &#8212;- (ii)<br \/>\nmultiply equation (i) by -1 and subtract the equations.<br \/>\n-1(x &#8211; 2y = 6)<br \/>\n-x + 2y = -6<br \/>\n-x + 2y &#8211; (-x + 4y) = -6 &#8211; 6<br \/>\n-x + 2y + x &#8211; 4y = -12<br \/>\n-2y = -12<br \/>\ny = 6<br \/>\nPut y = 6 in (i)<br \/>\nx &#8211; 2(6) = 6<br \/>\nx &#8211; 12 = 6<br \/>\nx = 6 + 12<br \/>\nx = 18<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>SOLVING A SYSTEM OF LINEAR EQUATIONS<\/strong><br \/>\n<strong>Solve the system by elimination. Check your solution.<\/strong><\/p>\n<p>Question 8.<br \/>\n2x + y = 4<br \/>\n-2x + 2y = 5<\/p>\n<p>Answer:<br \/>\nThe solution set is (1\/2, 3)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n2x + y = 4 &#8212;&#8212; (i)<br \/>\n-2x + 2y = 5 &#8212;&#8211; (ii)<br \/>\nAdd equations<br \/>\n2x + y &#8211; 2x + 2y = 4 + 5<br \/>\n3y = 9<br \/>\ny = 3<br \/>\nSubstitute y = 3 in (i)<br \/>\n2x + 3 = 4<br \/>\n2x = 4 &#8211; 3<br \/>\n2x = 1<br \/>\nx = 1\/2<br \/>\nSubstitute x = 1\/2, y = 3 in (ii)<br \/>\n-2(1\/2) + 2(3) = -1 + 6 = 5<br \/>\nSo, the solution set is (1\/2, 3)<\/p>\n<p>Question 9.<br \/>\n-x + y = 1<br \/>\n-3x + y =7<\/p>\n<p>Answer:<br \/>\nThe solution set is (-3, -2).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n-x + y = 1 &#8212;- (i)<br \/>\n-3x + y =7 &#8212;&#8211; (ii)<br \/>\nSubtract equations<br \/>\n-x + y &#8211; (-3x + y) = 1 &#8211; 7<br \/>\n-x + y + 3x &#8211; y = -6<br \/>\n2x = -6<br \/>\nx = -3<br \/>\nSubstitute x = -3 in (ii)<br \/>\n-3(-3) + y = 7<br \/>\n9 + y = 7<br \/>\ny = 7 &#8211; 9<br \/>\ny = -2<br \/>\nSubstitute x = -3, y = -2 in (i)<br \/>\n-(-3) &#8211; 2 = 3 &#8211; 2 = 1<br \/>\nSo, the solution set is (-3, -2).<\/p>\n<p>Question 10.<br \/>\ny = -2x + 3<br \/>\n4x &#8211; 5y = 13<\/p>\n<p>Answer:<br \/>\nThe solution set is (2, -1).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\ny = -2x + 3<br \/>\n2x + y = 3 &#8212;&#8211; (i)<br \/>\n4x &#8211; 5y = 13 &#8212;&#8211; (ii)<br \/>\nMultiply equation (i) by 2 and subtract<br \/>\n2(2x + y = 3)<br \/>\n4x + 2y = 6<br \/>\n4x + 2y &#8211; (4x &#8211; 5y) = 6 &#8211; 13<br \/>\n4x + 2y &#8211; 4x + 5y = -7<br \/>\n7y = -7<br \/>\ny = -1<br \/>\nSubstitute y = -1 in (i)<br \/>\n2x &#8211; 1 = 3<br \/>\n2x = 4<br \/>\nx = 2<br \/>\nSubstitute x = 2, y = -1 in (ii)<br \/>\n4(2) &#8211; 5(-1) = 8 + 5 = 13<br \/>\nSo, the solution set is (2, -1).<\/p>\n<p><strong>CHOOSING A SOLUTION METHOD<\/strong><br \/>\n<strong>Solve the system. Explain your choice of method.<\/strong><\/p>\n<p>Question 11.<br \/>\ny = 6x &#8211; 1<br \/>\ny = 3x &#8211; 4<\/p>\n<p>Answer:<br \/>\nThe solution set is (-1, -7)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\ny = 6x &#8211; 1 &#8212;- (i)<br \/>\ny = 3x &#8211; 4 &#8212;&#8211; (ii)<br \/>\nEquating both the equations<br \/>\n6x &#8211; 1 = 3x &#8211; 4<br \/>\n6x &#8211; 3x = -4 + 1<br \/>\n3x = -3<br \/>\nx = -3\/3<br \/>\nx = -1<br \/>\nSubstitute x = -1 in equation (i)<br \/>\ny = 6(-1) &#8211; 1<br \/>\ny = -7<br \/>\nSo, the solution set is (-1, -7)<\/p>\n<p>Question 12.<br \/>\n3x = y + 2<br \/>\n3x + 2y = 5<\/p>\n<p>Answer:<br \/>\nThe solution set is (1, 1).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n3x = y + 2 &#8212;- (i)<br \/>\n3x + 2y = 5 &#8212;&#8211; (ii)<br \/>\nSubstitute equation (i) in (ii)<br \/>\ny + 2 + 2y = 5<br \/>\n3y = 5 &#8211; 2<br \/>\n3y = 3<br \/>\ny = 1<br \/>\nSubstitute y = 1 in (i)<br \/>\n3x = 1 + 2<br \/>\n3x = 3<br \/>\nx = 1<br \/>\nSo, the solution set is (1, 1).<\/p>\n<p>Question 13.<br \/>\n2x &#8211; y = 7<br \/>\nx + y = 5<\/p>\n<p>Answer:<br \/>\nThe solution set is (4, 1).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n2x &#8211; y = 7 &#8212;- (i)<br \/>\nx + y = 5 &#8212;- (ii)<br \/>\nAdd equations<br \/>\n2x &#8211; y + x + y = 7 + 5<br \/>\n3x = 12<br \/>\nx = 4<br \/>\nSubstitute x = 4 in (ii)<br \/>\n4 + y = 5<br \/>\ny = 5 &#8211; 4<br \/>\ny = 1<br \/>\nSo, the solution set is (4, 1).<\/p>\n<p>Question 14.<br \/>\n<strong>WHICH ONE DOESN&#8217;T BELONG?<\/strong><br \/>\nWhich system does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32579\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-37.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 37\" width=\"480\" height=\"68\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-37.png 480w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-37-300x43.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><\/p>\n<p>Answer:<br \/>\n2x + 3y = 11, 3x &#8211; 2y = 10 is does not belong to other three.<\/p>\n<p>Explanation:<br \/>\n1. 3x + 3y = 3 &#8212;- (i)<br \/>\n2x &#8211; 3y = 7 &#8212;- (ii)<br \/>\nAdd equations<br \/>\n3x + 3y + 2x &#8211; 3y = 3 + 7<br \/>\n5x = 10<br \/>\nx = 2<br \/>\nSubstitute x = 2 in (ii)<br \/>\n2(2) &#8211; 3y = 7<br \/>\n4 &#8211; 3y = 7<br \/>\n-3y = 7 &#8211; 4<br \/>\n-3y = 3<br \/>\ny = -1<br \/>\nThe solution set is (2, -1).<br \/>\n2. -2x + y = 6 &#8212; (i)<br \/>\n2x &#8211; 3y = -10 &#8212; (ii)<br \/>\nAdd equations<br \/>\n-2x + y + 2x &#8211; 3y = 6 &#8211; 10<br \/>\n-2y = -4<br \/>\ny = 2<br \/>\nSubstitute y = 2 in (i)<br \/>\n-2x + 2 = 6<br \/>\n-2x = 4<br \/>\nx = -2<br \/>\nThe solution set is (-2, 2)<br \/>\n3. 2x + 3y = 11 &#8212;- (i)<br \/>\n3x &#8211; 2y = 10<br \/>\n3x = 10 + 2y<br \/>\nx = (10 + 2y)\/3<br \/>\nSubstitute x = (10 + 2y)\/3 in (i)<br \/>\n2(10 + 2y)\/3 + 3y = 11<br \/>\n20 + 4y + 9y = 33<br \/>\n20 + 13y = 33<br \/>\n13y = 33 &#8211; 20<br \/>\ny = 1<br \/>\nPut y = 1 in (i)<br \/>\n2x + 3 = 11<br \/>\n2x = 11 &#8211; 3<br \/>\n2x = 8<br \/>\nx = 4<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 15.<br \/>\nA \ufb01tness instructor purchases exercise bikes and treadmills for two gyms. For the \ufb01rst gym, 2 exercise bikes and 3 treadmills cost $2200. For the second gym, 3 exercise bikes and 4 treadmills cost $3000. How much does a treadmill cost?<\/p>\n<p>Answer:<br \/>\nThe cost of a treadmill is $600.<\/p>\n<p>Explanation:<br \/>\nLet x and y be the price of exercise bikes and treadmills, respectively<br \/>\nUsing the fact that<br \/>\nTotal cost = cost of exercise bike . Number of bikes in a gym + Cost of treadmill . Number of treadmills in a gym<br \/>\n2x + 3y = 2200 &#8212;- (i)<br \/>\n3x + 4y = 3000 &#8212;&#8211; (ii)<br \/>\nMultiply (i) by 3 and (ii) by 2<br \/>\n3(2x + 3y = 2200)<br \/>\n6x + 9y = 6600 &#8212;- (iii)<br \/>\n2(3x + 4y = 3000)<br \/>\n6x + 8y = 6000 &#8212;&#8211; (iv)<br \/>\nSubtract equations<br \/>\n6x + 9y &#8211; 6x &#8211; 8y = 6600 &#8211; 6000<br \/>\ny = 600<br \/>\nThe cost of treadmill is $600.<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nAt your school, cooking club members raise $5 per member for a charity, and woodshop club members raise $10 per member for a different charity. The cooking club has three times as many members as the woodshop club. The difference in the number of members in the two clubs is 12 members. How much does each club raise?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32580\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-38.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 38\" width=\"206\" height=\"138\" \/><\/p>\n<p>Answer:<br \/>\nMoney raised for charity by the cooking club is $90, Money raised for charity by the woodshop club $60.<\/p>\n<p>Explanation:<br \/>\nLet x and y be the number of members of the cooking club and woodshop club<br \/>\nThe cooking club has three times as many members as the woodshop club.<br \/>\nx = 3y<br \/>\nThe difference in the number of members in the two clubs is 12 members.<br \/>\nx &#8211; y = 12<br \/>\n3y &#8211; y = 12<br \/>\n2y = 12<br \/>\ny = 6<br \/>\nSo, x = 3(6) = 18<br \/>\nMoney raised for charity by cooking club = Number of members in a cooking club. Charity per member of cooking club<br \/>\n= x . 5<br \/>\n= 18 . 5<br \/>\n= $90<br \/>\nMoney raised for charity by woodshop club = Number of members in woodshop club. Charity per member of woodshop club<br \/>\n= y . 10<br \/>\n= 6 . 10<br \/>\n= $60<\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_by_Elimination_Homework_&amp;_Practice_5.3\"><\/a>Solving Systems of Linear Equations by Elimination Homework &amp; Practice 5.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Solve the system by substitution. Check your solution.<\/strong><\/p>\n<p>Question 1.<br \/>\nx = 5 &#8211; y<br \/>\nx &#8211; y = 3<\/p>\n<p>Answer:<br \/>\nThe solution set is (4, 1).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\nx = 5 &#8211; y &#8212;- (i)<br \/>\nx &#8211; y = 3 &#8212;- (ii)<br \/>\nSubstitute equation (i) in (ii)<br \/>\n5 &#8211; y &#8211; y = 3<br \/>\n5 &#8211; 2y = 3<br \/>\n5 &#8211; 3 = 2y<br \/>\n2 = 2y<br \/>\ny = 1<br \/>\nSubstitute y = 1 in (i)<br \/>\nx = 5 &#8211; 1<br \/>\nx = 4<br \/>\nSubstitute x = 4, y = 1 in (ii)<br \/>\n4 &#8211; 1 = 3<br \/>\nSo, the solution set is (4, 1).<\/p>\n<p>Question 2.<br \/>\nx &#8211; 5y = 1<br \/>\n-x + y = 7<\/p>\n<p>Answer:<br \/>\nThe solution set is (-9, -2)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\nx &#8211; 5y = 1<br \/>\nx = 1 + 5y &#8212;- (i)<br \/>\n-x + y = 7 &#8212;- (ii)<br \/>\nSubstitute (i) in (ii)<br \/>\n-1 &#8211; 5y + y = 7<br \/>\n-1 &#8211; 4y = 7<br \/>\n-4y = 7 + 1<br \/>\n-4y = 8<br \/>\ny = -2<br \/>\nSubstitute y = -2 in (i)<br \/>\nx = 1 + 5(-2)<br \/>\nx = 1 &#8211; 10<br \/>\nx = -9<br \/>\nSubstitute x = -9, y = -2<br \/>\n-(-9) &#8211; 2 = 9 &#8211; 2 = 7<br \/>\nSo, the solution set is (-9, -2)<\/p>\n<p>Question 3.<br \/>\nx + 6y = -2<br \/>\n-x = 3y &#8211; 10<\/p>\n<p>Answer:<br \/>\nThe solution set is (22, -4).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\nx + 6y = -2 &#8212;- (i)<br \/>\n-x = 3y &#8211; 10 &#8212;- (ii)<br \/>\nSubstitute (ii) in (i)<br \/>\n-3y + 10 + 6y = -2<br \/>\n3y + 10 = -2<br \/>\n3y = -2 &#8211; 10<br \/>\n3y = -12<br \/>\ny = -4<br \/>\nSubstitute y = -4 in (ii)<br \/>\n-x = 3(-4) &#8211; 10<br \/>\n-x = -12 &#8211; 10<br \/>\n-x = -22<br \/>\nx = 22<br \/>\nSubstitute x = 22, y = -4 in (i)<br \/>\n22 + 6(-4) = 22 &#8211; 24 = -2<br \/>\nSo, the solution set is (22, -4).<\/p>\n<p><strong>The vertices of a triangle are given. Draw the triangle and its image after a dilation with the given scale factor. Identify the type of dilation.<\/strong><\/p>\n<p>Question 4.<br \/>\nA(1, 1), B(1, 3), C(3, 1); k = 2<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-35.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 35\" width=\"963\" height=\"720\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-35.jpg 963w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-35-300x224.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-35-768x574.jpg 768w\" sizes=\"(max-width: 963px) 100vw, 963px\" \/><br \/>\nThe new triangle is larger than the original triangle so it&#8217;s an increase.<\/p>\n<p>Explanation:<br \/>\nThe vertices of a triangle are A(1, 1), B(1, 3), C(3, 1)<br \/>\nMultiply the coordinates by 2 and then graph the original and new coordinates.<br \/>\nNew coordinates are D(2, 2), E(2, 6), F(6, 2)<br \/>\nThe new triangle is larger than the original triangle so it&#8217;s an increase.<\/p>\n<p>Question 5.<br \/>\nD(-8, -4), E(-4, 8), F(0, 0); k = 0.5<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-36.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 36\" width=\"966\" height=\"717\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-36.jpg 966w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-36-300x223.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-36-768x570.jpg 768w\" sizes=\"(max-width: 966px) 100vw, 966px\" \/><br \/>\nThe new triangle is smaller than the original triangle so it&#8217;s a reduction.<\/p>\n<p>Explanation:<br \/>\nThe vertices of a triangle are D(-8, -4), E(-4, 8), F(0, 0)<br \/>\nMultiply the coordinates by 0.5 and then graph the original and new coordinates<br \/>\nThe new coordinates are A(-4, -2), B(-2, 4), C(0, 0)<br \/>\nThe new triangle is smaller than the original triangle so it&#8217;s a reduction.<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><br \/>\n<strong>SOLVING A SYSTEM ALGEBRAICALLY<\/strong><br \/>\n<strong>Explain how to obtain the equation 3x = 6 from the given system.<\/strong> (See Exploration 1, p. 211.)<\/p>\n<p>Question 6.<br \/>\n2x + y = 5<br \/>\nx &#8211; y = 1<\/p>\n<p>Answer:<br \/>\nAdd both equations<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n2x + y = 5 &#8212;&#8211; (i)<br \/>\nx &#8211; y = 1 &#8212;&#8211; (ii)<br \/>\nAdd both equations<br \/>\n2x + y + x &#8211; y = 5 + 1<br \/>\n3x = 6<\/p>\n<p>Question 7.<br \/>\n5x + 2y = 2<br \/>\nx + y = -2<\/p>\n<p>Answer:<br \/>\nMultiply the equation 2 by 2 and Subtract equation obtained equation from (i)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n5x + 2y = 2 &#8212;&#8211; (i)<br \/>\nx + y = -2 &#8212;&#8212; (ii)<br \/>\nMultiply the equation 2 by 2<br \/>\n2(x + y) = 2(-2)<br \/>\n2x + 2y = -4<br \/>\nSubtract equation obtained equation from (i)<br \/>\n5x + 2y &#8211; 2x &#8211; 2y = 2 + 4<br \/>\n3x = 6<\/p>\n<p>Question 8.<br \/>\n-x + y = -3<br \/>\n6x &#8211; 3y =15<\/p>\n<p>Answer:<br \/>\nMultiply the equation (i) by 3, Add equations (i) &amp; (iii)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n-x + y = -3 &#8212;- (i)<br \/>\n6x &#8211; 3y =15 &#8212;- (ii)<br \/>\nMultiply the equation (i) by 3<br \/>\n3(-x + y = -3)<br \/>\n-3x + 3y = -9 &#8212;- (ii)<br \/>\nAdd equation (i) &amp; (iii)<br \/>\n6x &#8211; 3y &#8211; 3x + 3y = 15 &#8211; 9<br \/>\n3x = 6<\/p>\n<p><strong>SOLVING A SYSTEM OF LINEAR EQUATIONS<\/strong><br \/>\n<strong>Solve the system by elimination. Check your solution.<\/strong><\/p>\n<p>Question 9.<br \/>\nx + 3y = 5<br \/>\n-x &#8211; y = -3<\/p>\n<p>Answer:<br \/>\nThe solution set is (2, 1).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\nx + 3y = 5 &#8212;- (i)<br \/>\n-x &#8211; y = -3 &#8212;&#8211; (ii)<br \/>\nAdd equations (i) &amp; (ii)<br \/>\nx + 3y &#8211; x &#8211; y = 5 &#8211; 3<br \/>\n2y = 2<br \/>\ny = 1<br \/>\nSubstitute y = 1 in (ii)<br \/>\n-x &#8211; 1 = -3<br \/>\n-x = -3 + 1<br \/>\n-x = -2<br \/>\nx = 2<br \/>\nSubstitute x = 2, y = 1 in (i)<br \/>\n2 + 3(1) = 2 + 3 = 5<br \/>\nSo, the solution set is (2, 1).<\/p>\n<p>Question 10.<br \/>\nx &#8211; 2y = -7<br \/>\n3x + 2y = 3<\/p>\n<p>Answer:<br \/>\nThe solution set is (-1, 3).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\nx &#8211; 2y = -7 &#8212;- (i)<br \/>\n3x + 2y = 3 &#8212;- (ii)<br \/>\nAdd equations (i), (ii)<br \/>\nx &#8211; 2y + 3x + 2y = -7 + 3<br \/>\n4x = -4<br \/>\nx = -1<br \/>\nSubstitute x = -1 in (i)<br \/>\n-1 &#8211; 2y = -7<br \/>\n-2y = -7 + 1<br \/>\n-2y = -6<br \/>\ny = 3<br \/>\nSubstitute x = -1, y = 3 in (i)<br \/>\n-1 &#8211; 2(3) = -1 &#8211; 6 = -7<br \/>\nSo, the solution set is (-1, 3).<\/p>\n<p>Question 11.<br \/>\n4x + 3y = -5<br \/>\n-x + 3y = -10<\/p>\n<p>Answer:<br \/>\nThe solution set is(1, -3).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n4x + 3y = -5 &#8212;- (i)<br \/>\n-x + 3y = -10 &#8212;- (ii)<br \/>\nSubtract equations (i), (ii)<br \/>\n4x + 3y &#8211; (-x + 3y) = -5 &#8211; (-10)<br \/>\n4x + 3y + x &#8211; 3y = -5 + 10<br \/>\n5x = 5<br \/>\nx = 1<br \/>\nSubstitute x = 1 in (ii)<br \/>\n-1 + 3y = -10<br \/>\n3y = -10 + 1<br \/>\n3y = -9<br \/>\ny = -3<br \/>\nSubstitute x = 1, y = -3 in (i)<br \/>\n4(1) + 3(-3) = 4 &#8211; 9 = -5<br \/>\nSo, the solution set is(1, -3).<\/p>\n<p>Question 12.<br \/>\n2x + 7y = 1<br \/>\n2x &#8211; 4y = 12<\/p>\n<p>Answer:<br \/>\nThe solution set is (4, -1).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n2x + 7y = 1 &#8212;- (i)<br \/>\n2x &#8211; 4y = 12 &#8212;&#8211; (ii)<br \/>\nSubtract equations (i), (ii)<br \/>\n2x &#8211; 4y &#8211; (2x + 7y) = 12 &#8211; 1<br \/>\n2x &#8211; 4y &#8211; 2x &#8211; 7y = 11<br \/>\n-11y = 11<br \/>\ny = -1<br \/>\nSubstitute y = -1 in (ii)<br \/>\n2x &#8211; 4(-1) = 12<br \/>\n2x + 4 = 12<br \/>\n2x = 12 &#8211; 4<br \/>\n2x = 8<br \/>\nx = 4<br \/>\nSubstitute x = 4, y = -1 in (i)<br \/>\n2(4) + 7(-1) = 8 &#8211; 7 = 1<br \/>\nSo, the solution set is (4, -1).<\/p>\n<p>Question 13.<br \/>\n2x + 5y = 16<br \/>\n3x &#8211; 5y = -1<\/p>\n<p>Answer:<br \/>\nThe solution set is (3, 2).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n2x + 5y = 16 &#8212;- (i)<br \/>\n3x &#8211; 5y = -1 &#8212;&#8211; (ii)<br \/>\nAdd both equations<br \/>\n2x + 5y + 3x &#8211; 5y = 16 &#8211; 1<br \/>\n5x = 15<br \/>\nx = 3<br \/>\nSubstitute x = 3 in (i)<br \/>\n2(3) + 5y = 16<br \/>\n5y = 16 &#8211; 6<br \/>\n5y = 10<br \/>\ny = 2<br \/>\nSubstitute x = 3, y = 2 in (ii)<br \/>\n3(3) &#8211; 5(2) = 9 &#8211; 10 = -1<br \/>\nSo, the solution set is (3, 2).<\/p>\n<p>Question 14.<br \/>\n3x &#8211; 2y = 4<br \/>\n6x &#8211; 2y = -2<\/p>\n<p>Answer:<br \/>\nThe solution set is (-2, -5).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n3x &#8211; 2y = 4 &#8212;&#8211; (i)<br \/>\n6x &#8211; 2y = -2 &#8212;&#8211; (ii)<br \/>\nSubtract equations<br \/>\n3x &#8211; 2y &#8211; (6x &#8211; 2y) = 4 &#8211; (-2)<br \/>\n3x &#8211; 2y &#8211; 6x + 2y = 4 + 2<br \/>\n-3x = 6<br \/>\nx = -2<br \/>\nSubstitute x = -2 in (i)<br \/>\n3(-2) &#8211; 2y = 4<br \/>\n-6 &#8211; 2y = 4<br \/>\n-2y = 4 + 6<br \/>\n-2y = 10<br \/>\ny = -5<br \/>\nSubstitute x = -2, y = -5 in (ii)<br \/>\n6(-2) &#8211; 2(-5) = -12 + 10 = -2<br \/>\nSo, the solution set is (-2, -5).<\/p>\n<p>Question 15.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend solves the system. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32581\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-39.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 39\" width=\"248\" height=\"178\" \/><\/p>\n<p>Answer:<br \/>\nWrong.<\/p>\n<p>Explanation:<br \/>\nThe given equations are 5x + 2y = 9 &#8212;- (i)<br \/>\n3x &#8211; 2y = -1 &#8212;- (ii)<br \/>\nAdd both equations<br \/>\n5x + 2y + 3x &#8211; 2y = 9 &#8211; 1<br \/>\n8x = 8<br \/>\nx = 1<br \/>\nPut x = 1 in (ii)<br \/>\n3(1) &#8211; 2y = -1<br \/>\n3 &#8211; 2y = -1<br \/>\n-2y = -1 &#8211; 3<br \/>\n-2y = -4<br \/>\ny = 2<br \/>\nSo, the solution set is (1, 2).<\/p>\n<p>Question 16.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou and your friend are selling raffle tickets for a new laptop. You sell 14 more tickets than your friend sells. Together, you and your friend sell 58 tickets.<br \/>\na. Write a system of linear equations that represents this situation.<br \/>\nb. How many tickets do each of you sell?<\/p>\n<p>Answer:<br \/>\na. x = 14 + y, x + y = 58<br \/>\nb. The number of tickers you sell is 36, the number of tickets your friend sells is 22.<\/p>\n<p>Explanation:<br \/>\na. Let x be the number of tickets you sell and let y be the number of tickets your friend sells.<br \/>\nYou sell 14 more tickets than your friend sells<br \/>\nx = 14 + y &#8212;- (i)<br \/>\nTogether, you and your friend sell 58 tickets.<br \/>\nx + y = 58 &#8212;- (ii)<br \/>\nb. Substitute equation (i) in (ii)<br \/>\n14 + y + y = 58<br \/>\n14 + 2y = 58<br \/>\n2y = 58 &#8211; 14<br \/>\n2y = 44<br \/>\ny = 44\/2<br \/>\ny = 22<br \/>\nSubstitute y = 22 in (i)<br \/>\nx = 14 + 22<br \/>\nx = 36<br \/>\nSo, The number of tickers you sell is 36, the number of tickets your friend sells is 22.<\/p>\n<p>Question 17.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou can jog around your block twice and the park once in 10 minutes. You can jog around your block twice and the park 3 times in 22 minutes. Write a system of linear equations that represents this situation. How long does it take you to jog around the park?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32582\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-40.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 40\" width=\"170\" height=\"405\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-40.png 170w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-40-126x300.png 126w\" sizes=\"(max-width: 170px) 100vw, 170px\" \/><\/p>\n<p>Answer:<br \/>\nThe system of linear equations are 2x + y = 10, 2x + 3y = 22<br \/>\nIt takes 6 minutes to jog around the park.<\/p>\n<p>Explanation:<br \/>\nLet x be the number of minutes it takes to jog around the block and y be the number of minutes it takes to jog around the park<br \/>\nYou can jog around your block twice and the park once in 10 minutes<br \/>\n2x + y = 10 &#8212;- (i)<br \/>\nYou can jog around your block twice and the park 3 times in 22 minutes<br \/>\n2x + 3y = 22 &#8212;- (ii)<br \/>\nSubtract equations<br \/>\n2x + y &#8211; 2x &#8211; 3y = 10 &#8211; 22<br \/>\n-2y = -12<br \/>\ny = 6<br \/>\nSubstitute y = 6 in (i)<br \/>\n2x + 6 = 10<br \/>\n2x = 10 &#8211; 6<br \/>\n2x = 4<br \/>\nx = 2<br \/>\nSo, it takes 6 minutes to jog around the park.<\/p>\n<p><strong>SOLVING A SYSTEM OF LINEAR EQUATIONS<\/strong><br \/>\n<strong>Solve the system by elimination. Check your solution.<\/strong><\/p>\n<p>Question 18.<br \/>\n2x &#8211; y = 0<br \/>\n3x &#8211; 2y = -3<\/p>\n<p>Answer:<br \/>\nThe solution set is (3, 6).<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\n2x &#8211; y = 0 &#8212;- (i)<br \/>\n3x &#8211; 2y = -3 &#8212;&#8211; (ii)<br \/>\nMultiply equation (i) by 2<br \/>\n2(2x &#8211; y = 0)<br \/>\n4x &#8211; 2y = 0 &#8212;- (iii)<br \/>\nSubtract equation (ii) from (iii)<br \/>\n4x &#8211; 2y &#8211; (3x &#8211; 2y) = 0 &#8211; (-3)<br \/>\n4x &#8211; 2y &#8211; 3x + 2y = 3<br \/>\nx = 3<br \/>\nSubstitute x = 3 in (i)<br \/>\n2(3) &#8211; y = 0<br \/>\n6 &#8211; y = 0<br \/>\ny = 6<br \/>\nSubstitute x = 3, y = 6 in (i)<br \/>\n2(3) &#8211; 6 = 6 &#8211; 6 = 0<br \/>\nSo, the solution set is (3, 6).<\/p>\n<p>Question 19.<br \/>\nx + 4y = 1<br \/>\n3x + 5y = 10<\/p>\n<p>Answer:<br \/>\nThe solution set is (5, -1).<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\nx + 4y = 1 &#8212;- (i)<br \/>\n3x + 5y = 10 &#8212;- (ii)<br \/>\nMultiply equation (i) by 3<br \/>\n3(x + 4y = 1)<br \/>\n3x + 12y = 3 &#8212;- (iii)<br \/>\nSubtract equation (iii) from (ii)<br \/>\n3x + 5y &#8211; (3x + 12y) = 10 &#8211; 3<br \/>\n3x + 5y &#8211; 3x &#8211; 12y = 7<br \/>\n-7y = 7<br \/>\ny = -1<br \/>\nSubstitute y = -1 in (i)<br \/>\nx + 4(-1) = 1<br \/>\nx &#8211; 4 = 1<br \/>\nx = 1 + 4<br \/>\nx = 5<br \/>\nSubstitute x = 5, y = -1 in (i)<br \/>\n5 + 4(-1) = 5 &#8211; 4 = 1<br \/>\nSo, the solution set is (5, -1).<\/p>\n<p>Question 20.<br \/>\n-2x + 3y = 7<br \/>\n5x + 8y = -2<\/p>\n<p>Answer:<br \/>\nThe solution set is (-2, 1).<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\n-2x + 3y = 7 &#8212;- (i)<br \/>\n5x + 8y = -2 &#8212;&#8211; (ii)<br \/>\nMultiply equation (i) by 5 and equation (ii) by 2<br \/>\n5(-2x + 3y = 7)<br \/>\n-10x + 15y = 35 &#8212;- (iii)<br \/>\n2(5x + 8y = -2)<br \/>\n10x + 16y = -4 &#8212;- (iv)<br \/>\nAdd equations (iii) &amp; (iv)<br \/>\n-10x + 15y + 10x + 16y = 35 &#8211; 4<br \/>\n31y = 31<br \/>\ny = 1<br \/>\nSubstitute y = 1 in (i)<br \/>\n-2x + 3(1) = 7<br \/>\n-2x = 7 &#8211; 3<br \/>\n-2x = 4<br \/>\nx = -2<br \/>\nSubstitute x = -2, y = 1 in (ii)<br \/>\n5(-2) + 8(1) = -10 + 8 = -2<br \/>\nSo, the solution set is (-2, 1).<\/p>\n<p>Question 21.<br \/>\n3x + 3 = 3y<br \/>\n2x &#8211; 6y = 2<\/p>\n<p>Answer:<br \/>\nThe solution set is (-2, -1).<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\n3x + 3 = 3y &#8212;- (i)<br \/>\n2x &#8211; 6y = 2 &#8212;- (ii)<br \/>\nMultiply equation (i) by 2<br \/>\n2(3x + 3 = 3y)<br \/>\n6x + 6 = 6y<br \/>\n6x &#8211; 6y = -6 &#8212;- (iii)<br \/>\nSubtract equations (ii) &amp; (iii)<br \/>\n2x &#8211; 6y &#8211; 6x + 6y = 2 + 6<br \/>\n-4x = 8<br \/>\nx = -2<br \/>\nSubstitute x = -2 in (i)<br \/>\n3(-2) + 3 = 3y<br \/>\n-6 + 3 = 3y<br \/>\n-3 = 3y<br \/>\ny = -1<br \/>\nSubstitute x = -2, y = -1 in (i)<br \/>\n3(-2) + 3 = 3(-1)<br \/>\n-6 + 3 = -3<br \/>\nSo, the solution set is (-2, -1).<\/p>\n<p>Question 22.<br \/>\n2x &#8211; 6 = 4y<br \/>\n7y =-3x + 9<\/p>\n<p>Answer:<br \/>\nThe solution set is (3, 0).<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\n2x &#8211; 6 = 4y<br \/>\n2x &#8211; 4y = 6 &#8212;- (i)<br \/>\n7y = -3x + 9<br \/>\n3x + 7y = 9 &#8212;- (ii)<br \/>\nMultiply (i) by 7 and (ii) by 4<br \/>\n7(2x &#8211; 4y = 6)<br \/>\n14x &#8211; 28y = 42 &#8212;- (iii)<br \/>\n4(3x + 7y = 9)<br \/>\n12x + 28y = 36 &#8212;- (iv)<br \/>\nAdd equations (iii) &amp; (iv)<br \/>\n14x &#8211; 28y + 12x + 28y = 42 + 36<br \/>\n26x = 78<br \/>\nx = 78\/26<br \/>\nx = 3<br \/>\nSubstitute x = 3 in (i)<br \/>\n2(3) &#8211; 4y = 6<br \/>\n6 &#8211; 4y = 6<br \/>\n6 &#8211; 6 = 4y<br \/>\ny = 0<br \/>\nSubstitute x = 3, y = 0 in (i)<br \/>\n2(3) &#8211; 4(0) = 6 &#8211; 0 = 6<br \/>\nSo, the solution set is (3, 0).<\/p>\n<p>Question 23.<br \/>\n5x = 4y + 8<br \/>\n3y = 3x &#8211; 3<\/p>\n<p>Answer:<br \/>\nThe solution set is (4, 3).<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\n5x = 4y + 8<br \/>\n5x &#8211; 4y = 8 &#8212; (i)<br \/>\n3y = 3x &#8211; 3<br \/>\n3x &#8211; 3y = 3 &#8212;- (ii)<br \/>\nMultiply (i) by 3 and (ii) by 4<br \/>\n3(5x &#8211; 4y = 8)<br \/>\n15x &#8211; 12y = 24 &#8212; (iii)<br \/>\n4(3x &#8211; 3y = 3)<br \/>\n12x &#8211; 12y = 12 &#8212;- (iv)<br \/>\nSubtract obtained equations<br \/>\n15x &#8211; 12y &#8211; 12x + 12y = 24 &#8211; 12<br \/>\n3x = 12<br \/>\nx = 4<br \/>\nSubstitute x = 4 in (ii)<br \/>\n3(4) &#8211; 3y = 3<br \/>\n12 &#8211; 3y = 3<br \/>\n-3y = 3 &#8211; 12<br \/>\n-3y = -9<br \/>\ny = 3<br \/>\nSubstitute x = 4, y = 3 in (ii)<br \/>\n3(4) &#8211; 3(3) = 12 &#8211; 9 = 3<br \/>\nSo, the solution set is (4, 3).<\/p>\n<p>Question 24.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend solves the system. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32583\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-41.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 41\" width=\"540\" height=\"160\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-41.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-41-300x89.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Answer:<br \/>\nWrong.<\/p>\n<p>Explanation:<br \/>\nGiven equations are<br \/>\nx + y = 1 &#8212; (i)<br \/>\n5x + 3y = -3 (ii)<br \/>\nMultiply equation (i) by -5<br \/>\n-5(x + y = 1)<br \/>\n-5x &#8211; 5y = -5 &#8212; (iii)<br \/>\nAdd equations (iii) &amp; (ii)<br \/>\n-5x &#8211; 5y + 5x + 3y = -3 &#8211; 5<br \/>\n-2y = -8<br \/>\ny = 4<br \/>\nPut y = 4 in (i)<br \/>\nx + 4 = 1<br \/>\nx = 1 &#8211; 4 = -3<br \/>\nSo, the solution set is (-3, 4).<\/p>\n<p><strong>CHOOSING A SOLUTION METHOD<\/strong><br \/>\n<strong>Solve the system. Explain your choice of method.<\/strong><\/p>\n<p>Question 25.<br \/>\nx + y = 4<br \/>\nx &#8211; y = 4<\/p>\n<p>Answer:<br \/>\nThe solution set is (4, 0).<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\nx + y = 4 &#8212; (i)<br \/>\nx &#8211; y = 4 &#8212; (ii)<br \/>\nAdd equations<br \/>\nx + y + x &#8211; y = 4 + 4<br \/>\n2x = 8<br \/>\nx = 4<br \/>\nSubstitute x = 4 in (i)<br \/>\n4 + y = 4<br \/>\ny = 4 &#8211; 4<br \/>\ny = 0<br \/>\nSo, the solution set is (4, 0).<\/p>\n<p>Question 26.<br \/>\ny = x &#8211; 3<br \/>\ny = -2x + 3<\/p>\n<p>Answer:<br \/>\nThe solution set is (2, -1).<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\ny = x &#8211; 3 &#8212; (i)<br \/>\ny = -2x + 3 &#8212; (ii)<br \/>\nEquate both equations<br \/>\nx &#8211; 3 = -2x + 3<br \/>\nx + 2x = 3 + 3<br \/>\n3x = 6<br \/>\nx = 2<br \/>\nSubstitute x = 2 in (i)<br \/>\ny = 2 &#8211; 3<br \/>\ny = -1<br \/>\nSo, the solution set is (2, -1).<\/p>\n<p>Question 27.<br \/>\nx + 2y = 0<br \/>\n2x &#8211; y = 4<\/p>\n<p>Answer:<br \/>\nThe solution set is (8\/5, -4\/5)<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\nx + 2y = 0 &#8212;- (i)<br \/>\n2x &#8211; y = 4 &#8212;- (ii)<br \/>\ny = 2x &#8211; 4<br \/>\nSubstitute y = 2x &#8211; 4 in (i)<br \/>\nx + 2(2x &#8211; 4) = 0<br \/>\nx + 4x &#8211; 8 = 0<br \/>\n5x = 8<br \/>\nx = 8\/5<br \/>\nSubstitute x = 8\/5 in (i)<br \/>\n8\/5 + 2y = 0<br \/>\n2y = -8\/5<br \/>\ny = -4\/5<br \/>\nSo, the solution set is (8\/5, -4\/5)<\/p>\n<p>Question 28.<br \/>\ny + 5x = 1<br \/>\n5y &#8211; x = 5<\/p>\n<p>Answer:<br \/>\nThe solution set is (0, 1).<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\ny + 5x = 1 &#8212;- (i)<br \/>\n5y &#8211; x = 5 &#8212;- (ii)<br \/>\n5y &#8211; 5 = x<br \/>\nSubstitute x = 5y &#8211; 5 in (i)<br \/>\ny + 5(5y &#8211; 5) = 1<br \/>\ny + 25y &#8211; 25= 1<br \/>\n26y = 1 + 25<br \/>\n26y = 26<br \/>\ny = 1<br \/>\nSubstitute y = 1 in (i)<br \/>\n1 + 5x = 1<br \/>\n5x = 0<br \/>\nx = 0<br \/>\nSo, the solution set is (0, 1).<\/p>\n<p>Question 29.<br \/>\n2 = x &#8211; 3y<br \/>\n-2x + y = 4<\/p>\n<p>Answer:<br \/>\nThe solution set is (-14\/5, -8\/5)<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\n2 = x &#8211; 3y<br \/>\nx = 2 + 3y &#8212; (i)<br \/>\n-2x + y = 4 &#8212;- (ii)<br \/>\nSubstitute (i) in (ii)<br \/>\n-2(2 + 3y) + y = 4<br \/>\n-4 &#8211; 6y + y = 4<br \/>\n-5y = 4 + 4<br \/>\ny = -8\/5<br \/>\nSubstitute y = -8\/5 in (i)<br \/>\nx = 2 + 3(-8\/5)<br \/>\nx = 2 &#8211; 24\/5<br \/>\nx = -14\/5<br \/>\nSo, the solution set is (-14\/5, -8\/5)<\/p>\n<p>Question 30.<br \/>\n8x + 5y = 6<br \/>\n8x = 3 &#8211; 2y<\/p>\n<p>Answer:<br \/>\nThe solution set is (1\/8, 1).<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\n8x + 5y = 6 &#8212;- (i)<br \/>\n8x = 3 &#8211; 2y &#8212;- (ii)<br \/>\nSubstitute (ii) in (i)<br \/>\n3 &#8211; 2y + 5y = 6<br \/>\n3y = 6 &#8211; 3<br \/>\n3y = 3<br \/>\ny = 1<br \/>\nSubstitute y = 1 in (ii)<br \/>\n8x = 3 &#8211; 2(1)<br \/>\n8x = 1<br \/>\nx = 1\/8<br \/>\nSo, the solution set is (1\/8, 1).<\/p>\n<p><strong>NUMBER SENSE<\/strong><br \/>\n<strong>For what value of a might you choose to solve the system by elimination? Explain.<\/strong><\/p>\n<p>Question 31.<br \/>\n4x &#8211; y = 3<br \/>\nax + 10y = 6<\/p>\n<p>Answer:<br \/>\nIf a is 4 or -4 it is easy to solve the systems of linear equations using the elimination method as by just subtracting or adding the equations, we can eliminate x.<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\n4x &#8211; y = 3<br \/>\nax + 10y = 6<br \/>\nIf a is 4 or -4 it is easy to solve the systems of linear equations using the elimination method as by just subtracting or adding the equations, we can eliminate x.<\/p>\n<p>Question 32.<br \/>\nx &#8211; 7y = 6<br \/>\n-6x + ay = 9<\/p>\n<p>Answer:<br \/>\nIf a is 7 or -7 it is easy to solve the systems of linear equations using the elimination method as by just adding or subtracting the equations, we can eliminate x.<\/p>\n<p>Explanation:<br \/>\nThe systems of linear equations are<br \/>\nx &#8211; 7y = 6<br \/>\n-6x + ay = 9<br \/>\nIf a is 7 or -7 it is easy to solve the systems of linear equations using the elimination method as by just adding or subtracting the equations, we can eliminate x.<\/p>\n<p><strong>CRITICAL THINKING<\/strong><br \/>\n<strong>Determine whether the line through the \ufb01rst pair of points intersects the line through the second pair of points. Explain.<\/strong><\/p>\n<p>Question 33.<br \/>\nLine 1: (-2, 1), (2, 7)<br \/>\nLine 2: (-4, -1), (0, 5)<\/p>\n<p>Answer:<br \/>\nNo<\/p>\n<p>Explanation:<br \/>\nEquation of a line passing through points (x\u2081, y\u2081) and (x\u2082, y\u2082) is y &#8211; y\u2081 = (y\u2082 &#8211; y\u2081)\/(x\u2082 &#8211; x\u2081) (x &#8211; x\u2081)<br \/>\nSo, equation of line 1 is<br \/>\ny &#8211; 1 = (7 &#8211; 1)\/(2 + 2)(x + 2)<br \/>\ny &#8211; 1 = 6\/4 (x + 2)<br \/>\ny &#8211; 1 = 3\/2 (x + 2)<br \/>\n2(y &#8211; 1) = 3(x + 2)<br \/>\n2y &#8211; 2 = 3x + 6<br \/>\n3x &#8211; 2y = -2 &#8211; 6<br \/>\n3x &#8211; 2y = -8<br \/>\nEquation of line 2 is<br \/>\ny + 1 = (5 + 1)\/(0 + 4) (x + 4)<br \/>\ny + 1 = 6\/4 (x + 4)<br \/>\ny + 1 = 3\/2 (x + 4)<br \/>\n2(y + 1) = 3(x + 4)<br \/>\n2y + 2 = 3x + 12<br \/>\n3x &#8211; 2y = 2 &#8211; 12<br \/>\n3x &#8211; 2y = -10<br \/>\nAs the slope of the lines are same, but the consant is different, the lines are parallek to each other and there is no point of intersection.<\/p>\n<p>Question 34.<br \/>\nLine 1: (-2, 8), (0, 2)<br \/>\nLine 2: (3, -2), (6, 4)<\/p>\n<p>Answer:<br \/>\nYes<\/p>\n<p>Explanation:<br \/>\nEquation of a line passing through points (x\u2081, y\u2081) and (x\u2082, y\u2082) is y &#8211; y\u2081 = (y\u2082 &#8211; y\u2081)\/(x\u2082 &#8211; x\u2081) (x &#8211; x\u2081)<br \/>\nSo, line 1 is<br \/>\ny &#8211; 8 = (2 &#8211; 8)\/(0 + 2) (x + 2)<br \/>\ny &#8211; 8 = -6\/2 (x + 2)<br \/>\ny &#8211; 8 = -3(x + 2)<br \/>\ny &#8211; 8 = -3x &#8211; 6<br \/>\n3x + y = -6 + 8<br \/>\n3x + y = 2<br \/>\nLine 2 is<br \/>\ny + 2 = (4 + 2)\/(6 &#8211; 3) (x &#8211; 3)<br \/>\ny + 2 = 6\/3 (x &#8211; 3)<br \/>\ny + 2 = 2(x &#8211; 3)<br \/>\ny + 2 = 2x &#8211; 6<br \/>\n2x &#8211; y = 8<br \/>\nAs the slopes are different, so the lines intesect each other.<\/p>\n<p>Question 35.<br \/>\n<strong>REASONING<\/strong><br \/>\nTwo airplanes are \ufb02ying to the same airport. Their positions are shown in the graph. Write a system of linear equations that represents this situation. Solve the system by elimination to justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32584\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-42.png\" alt=\"Big Ideas Math Answer Key Grade 8 Chapter 5 Systems of Linear Equations 42\" width=\"670\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-42.png 670w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-8-Chapter-5-Systems-of-Linear-Equations-42-300x116.png 300w\" sizes=\"(max-width: 670px) 100vw, 670px\" \/><\/p>\n<p>Answer:<br \/>\nx = 6, y = 12.<\/p>\n<p>Explanation:<br \/>\nTo write the system we need the slope of each line and at least one point on the line. The two lines to consider will be the lines connecting the location of each plane to the airport they are flying to. It is also worth noting that the coordinates of the airport represent the point of intersection of the two lines and thus the solution to the system.<br \/>\nAirport (6, 12), Airplane 1 (2, 4), Airplane 2 (15, 9)<br \/>\nthe slope of the line connecting airplane 1 and the airport = (4 &#8211; 12)\/(2- 6)<br \/>\n= -8\/-4 = 2<br \/>\nThe line equation is y &#8211; 4 = 2(x -4)<br \/>\n2x &#8211; y = 0<br \/>\nslope of the line connecting airplane 2 and the airport = (4 &#8211; 9)\/(2 &#8211; 15)<br \/>\n= -5\/-13 = 5\/13<br \/>\nThe line equation is y &#8211; 9 = 5\/13 (x &#8211; 15)<br \/>\nx + 3y = 42<br \/>\nSo, the system of linear equations are<br \/>\n2x &#8211; y = 0 &#8212;- (i)<br \/>\nx + 3y = 42 &#8212;&#8211; (ii)<br \/>\nMultiply (ii) by 2<br \/>\n2(x + 3y = 42)<br \/>\n2x + 6y = 84 &#8212; (iii)<br \/>\nSubtract (iii) &amp; (i)<br \/>\n2x &#8211; y &#8211; 2x &#8211; 6y = 0 &#8211; 84<br \/>\n-7y = -84<br \/>\ny = 12<br \/>\nPut y = 12 in (i)<br \/>\n2x &#8211; 12 = 0<br \/>\nx = 6<br \/>\nWe have proven that the location of the airport is in fact the solution to our system.<\/p>\n<p>Question 36.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA laboratory uses liquid nitrogen tanks of two different sizes. The combined volume of 3 large tanks and 2 small tanks is 24 liters. The combined volume of 2 large tanks and 3 small tanks is 21 liters. What is the volume of each size of tank? Justify your answer.<\/p>\n<p>Answer:<br \/>\nThe volume of the large tank is 6 lit, the volume of the small tank is 3 lit.<\/p>\n<p>Explanation:<br \/>\nLet x and y be the volume of the large and small tank<br \/>\nThe combined volume of 3 large tanks and 2 small tanks is 24 liters. The combined volume of 2 large tanks and 3 small tanks is 21 liters<br \/>\nCombined volume = No of large tanks x volume of large tank + No of small tanks x volume of small tank<br \/>\n3x + 2y = 24 &#8212; (i)<br \/>\n2x + 3y = 21 &#8212;- (ii)<br \/>\nMultiply (i) by -2 and (ii) by 3<br \/>\n-2(3x + 2y = 24)<br \/>\n-6x &#8211; 4y = -48<br \/>\n3(2x + 3y = 21)<br \/>\n6x + 9y = 63<br \/>\nAdd obtained equations<br \/>\n-6x &#8211; 4y + 6x + 9y = -48 + 63<br \/>\n5y = 15<br \/>\ny = 3<br \/>\nPut y = 3 in (i)<br \/>\n3x + 6 = 24<br \/>\n3x = 24 &#8211; 6<br \/>\n3x = 18<br \/>\nx = 6<br \/>\nSo, the volume of the large tank is 6 lit, volume of the small tank is 3 lit.<\/p>\n<p>Question 37.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe table shows the numbers of correct answers on a practice standardized test. You score 86 points on the test and your friend scores 76 points. How many points is each type of question worth?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32585\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-43.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 43\" width=\"321\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-43.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-43-300x86.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><\/p>\n<p>Answer:<br \/>\nThe marks for correct multiple choice questions, short response questions are 2 and 4.<\/p>\n<p>Explanation:<br \/>\nLet x, y be the marks of multiple choice &amp; short response questions<br \/>\nTotal marks = no of correct MCQs x marks for correct MCQs + no of short response questions x marks for short response questions<br \/>\n23x + 10y = 86 &#8212; (i)<br \/>\n28x + 5y = 76 &#8212;- (ii)<br \/>\nMultiply (ii) by 2<br \/>\n2(28x + 5y = 76)<br \/>\n56x + 10y = 152 &#8212;- (iii)<br \/>\nSubtract (i) &amp; (iii)<br \/>\n23x + 10y &#8211; 56x &#8211; 10y = 86 &#8211; 152<br \/>\n-33x = -66<br \/>\nx = 2<br \/>\nPut x = 2 in (i)<br \/>\n23(2) + 10y = 86<br \/>\n10y = 86 &#8211; 46<br \/>\n10y = 40<br \/>\ny = 4<br \/>\nSo, the marks for correct multiple choice questions, short response questions are 2 and 4.<\/p>\n<p>Question 38.<br \/>\n<strong>LOGIC<\/strong><br \/>\nYou solve a system of equations in which x represents the number of adult memberships sold and y represents the number of student memberships sold. Can (-6, 24) be the solution to the system? Explain your reasoning.<\/p>\n<p>Answer:<br \/>\nIf x represents the number of adult tickets sold, then x must be a non-negative number since there can&#8217;t be a negative number of tickets sold.<br \/>\nTherefore (-6, 24) can&#8217;t be a solution since that would give x = 6.<\/p>\n<p>Explanation:<br \/>\nIf x represents the number of adult tickets sold, then x must be a non-negative number since there can&#8217;t be a negative number of tickets sold.<br \/>\nTherefore (-6, 24) can&#8217;t be a solution since that would give x = 6.<\/p>\n<p>Question 39.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe table shows the activities of two tourists at a vacation resort. You want to go parasailing for 1 hour and horseback riding for 2 hours. How much do you expect to pay?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32587\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-44.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 44\" width=\"435\" height=\"100\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-44.png 435w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-44-300x69.png 300w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32586\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-44.1.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 44.1\" width=\"239\" height=\"385\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-44.1.png 239w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-44.1-186x300.png 186w\" sizes=\"(max-width: 239px) 100vw, 239px\" \/><\/p>\n<p>Answer:<br \/>\nThe cost of parasailing for 1 hour and horseback riding for hours is $90.<\/p>\n<p>Explanation:<br \/>\nLet x and y represent per hour price for parasailing and horseback riding<br \/>\nTotal cost = no of hours of parasailing x per hour price for parasailing + no of hours of horseback riding x per hour price for horseback riding<br \/>\n2x + 5y = 205 &#8212;- (i)<br \/>\n3x + 3y = 240 &#8212; (ii)<br \/>\nMultiply (i) by 3 and (ii) by 2<br \/>\n3(2x + 5y = 205)<br \/>\n6x + 15y = 615 &#8212; (iii)<br \/>\n2(3x + 3y = 240)<br \/>\n6x + 6y = 480 &#8212;- (iv)<br \/>\nSubtract (iii) &amp; (iv)<br \/>\n6x + 15y &#8211; 6x &#8211; 6y = 615 &#8211; 480<br \/>\n9y = 135<br \/>\ny = 15<br \/>\nPut y = 15 in (i)<br \/>\n2x + 15(5) = 205<br \/>\n2x = 205 &#8211; 75<br \/>\n2x = 130<br \/>\nx = 65<br \/>\nSo, the Cost of parasailing for 1 hour and harseback riding for hours is x + 2y<br \/>\n= 65 + 2(15)<br \/>\n= $95.<\/p>\n<p>Question 40.<br \/>\n<strong>REASONING<\/strong><br \/>\nWrite a system of linear equations containing 2x + y = 0 and that has the solution (2, -4).<\/p>\n<p>Answer:<br \/>\nThe system of linear equations are 2x + y = 0, x &#8211; y = 6.<\/p>\n<p>Explanation:<br \/>\nThe equation of a line that passes through (2, -4) is y = mx + b<br \/>\n-4 = 2m + b<br \/>\nLet us take m slope as 1<br \/>\n-4 = 2 + b<br \/>\nb = -4 &#8211; 2<br \/>\nb = -6<br \/>\nSo, line is y = x &#8211; 6<br \/>\nSo, the system of linear equations are 2x + y = 0, x &#8211; y = 6.<\/p>\n<p>Question 41.<br \/>\n<strong>REASONING<\/strong><br \/>\nA metal alloy is a mixture of two or more metals. A jeweler wants to make 8 grams of 18-karat gold, which is 75% gold. The jeweler has an alloy that is 90% gold and an alloy that is 50% gold. old. How much of each alloy should the jeweler use?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32588\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-45.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 45\" width=\"280\" height=\"199\" \/><\/p>\n<p>Answer:<br \/>\nThe jeweler should use 5, 3 grams of first and second alloy.<\/p>\n<p>Explanation:<br \/>\nLet x, y be the amount of first &amp; second alloy<br \/>\nAmount of gold = percentage of gold in first alloy x amount of first alloy + percentage of gold in second alloy x amount of the second alloy<br \/>\nx + y = 8<br \/>\n0.9x + 0.5y = 6<br \/>\ny = 8 &#8211; x<br \/>\n0.9x + 0.5(8 &#8211; x) = 6<br \/>\n0.4x + 4 = 6<br \/>\n0.4x = 2<br \/>\nx = 5<br \/>\ny = 8 &#8211; 5<br \/>\ny = 3<br \/>\nThe jeweler should use 5, 3 grams of first and second alloy.<\/p>\n<p>Question 42.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nIt takes a powerboat traveling with the current 30 minutes to go 10 miles. The return trip takes 50 minutes traveling against the current. What is the speed of the current?<\/p>\n<p>Answer:<br \/>\nThe current speed is 4 miles per hour.<\/p>\n<p>Explanation:<br \/>\nLet r be the speed of the boat and w be the speed of water current<br \/>\ndownstream 10 = (r + w)30<br \/>\n1 = 3(r + w)<br \/>\n3r + 3w = 1 &#8212; (i)<br \/>\nUpstream 10 = (r &#8211; w)50<br \/>\n1 = 5(r &#8211; w)<br \/>\n5r &#8211; 5w = 1 &#8212;- (ii)<br \/>\nMultiply (i) by 5 and (ii) by 3 and add them<br \/>\n15r + 15w + 15r &#8211; 15w = 5 + 3<br \/>\n30r = 8<br \/>\nr = 4\/15<br \/>\nsubstitute r = 4\/15 in (ii)<br \/>\n5(4\/15) &#8211; 5w = 1<br \/>\n4\/3 &#8211; 5w = 1<br \/>\n-5w = -1\/3<br \/>\nw = 1\/15 miles per inute<br \/>\n= 1\/15 (60) = 4 miles per hour<br \/>\nThe current speed is 4 miles per hour.<\/p>\n<p>Question 43.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nSolve the system of equations by elimination.<br \/>\n2x &#8211; y + 3z = -1<br \/>\nx + 2y &#8211; 4z = -1<br \/>\ny &#8211; 2z = 0<\/p>\n<p>Answer:<br \/>\nThe solution set is (-1, 2, 1).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n2x &#8211; y + 3z = -1 &#8212;&#8211; (i)<br \/>\nx + 2y &#8211; 4z = -1 &#8212;- (ii)<br \/>\ny &#8211; 2z = 0 &#8212;&#8211; (iii)<br \/>\nSubstitute y = 2z in (i) &amp; (ii)<br \/>\n2x &#8211; 2z + 3z = -1<br \/>\n2x+ z = -1 &#8212;- (iv)<br \/>\nx + 4z &#8211; 4z = -1<br \/>\nx = -1<br \/>\nSubstitute x = -1 in (iv)<br \/>\n2(-1) + z = -1<br \/>\nz = -1 + 2<br \/>\nz = 1<br \/>\nSubstitute z = 1 in (iii)<br \/>\ny &#8211; 2 = 0<br \/>\ny = 2<br \/>\nSo, the solution set is (-1, 2, 1).<\/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>EXPLORATION 1<\/strong><br \/>\n<strong>Exploring Solutions of Systems<\/strong><br \/>\n<strong>Work with a partner. You spend $50 on a sewing machine to makedog backpacks. Each backpack costs you $15 for materials.<\/strong><br \/>\na. Represent the cost (in dollars) to make backpacks in the coordinate plane.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32589\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-46.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 46\" width=\"263\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-46.png 263w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-46-150x150.png 150w\" sizes=\"(max-width: 263px) 100vw, 263px\" \/><br \/>\nb. You charge $25 per backpack. How many backpacks do you have to break even sell to ? Use a graph to justify your answer.<br \/>\nc. Can you break even when you sell each backpack for $20? $15? Use graphs to justify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32590\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-47.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 47\" width=\"159\" height=\"188\" \/><br \/>\nd. Explain whether it is possible for a system of linear equations to have the numbers of solutions below.<\/p>\n<ul>\n<li>no solution<\/li>\n<li>exactly one solution<\/li>\n<li>exactly two solutions<\/li>\n<li>infinitely many solutions<\/li>\n<\/ul>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32592\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-48.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 48\" width=\"394\" height=\"247\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-48.png 394w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-48-300x188.png 300w\" sizes=\"(max-width: 394px) 100vw, 394px\" \/><\/p>\n<p><strong>5.4 Lesson<\/strong><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the system. Explain your choice of method.<\/strong><\/p>\n<p>Question 1.<br \/>\ny = -x + 3<br \/>\ny = -x + 5<\/p>\n<p>Answer:<br \/>\nThere is no solution.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = -x + 3<br \/>\ny = -x + 5<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50178\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-37.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 37\" width=\"667\" height=\"650\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-37.jpg 667w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-37-300x292.jpg 300w\" sizes=\"(max-width: 667px) 100vw, 667px\" \/><br \/>\nThe two lines are parallel to each other.<br \/>\nSo, there is no solution.<\/p>\n<p>Question 2.<br \/>\ny = -5x &#8211; 2<br \/>\n5x + y = 0<\/p>\n<p>Answer:<br \/>\nThe system has no solution.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = -5x &#8211; 2, 5x + y = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50179\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-38.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 38\" width=\"663\" height=\"654\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-38.jpg 663w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-38-300x296.jpg 300w\" sizes=\"(max-width: 663px) 100vw, 663px\" \/><br \/>\nThe two lines are parallel to each other.<br \/>\nSo, the system has no solution.<\/p>\n<p>Question 3.<br \/>\nx = 2y + 10<br \/>\n2x + 3y = -1<\/p>\n<p>Answer:<br \/>\nThe solution set is (4, -3)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are x = 2y + 10, 2x + 3y = -1<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50180\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-39.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 39\" width=\"540\" height=\"529\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-39.jpg 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-39-300x294.jpg 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><br \/>\nThe point of intersection of two lines is (4, -3)<br \/>\nSo, the solution set is (4, -3)<\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>Solve the system. Explain your choice of method.<\/strong><\/p>\n<p>Question 4<br \/>\nx + y = 3<br \/>\nx = y &#8211; 3<\/p>\n<p>Answer:<br \/>\nThe solution set is (0, 3).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\nx + y = 3 &#8212; (i)<br \/>\nx = y &#8211; 3 &#8212;- (ii)<br \/>\nSubstitute (ii) in (i)<br \/>\ny &#8211; 3 + y = 3<br \/>\n2y = 6<br \/>\ny = 3<br \/>\nSubstitute y = 3 in (ii)<br \/>\nx = 3 &#8211; 3<br \/>\nx = 0<br \/>\nSo, the solution set is (0, 3).<\/p>\n<p>Question 5.<br \/>\n2x + y = 5<br \/>\n4x + 2y = 0<\/p>\n<p>Answer:<br \/>\nThe system has no solution.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n2x + y = 5 &#8212;- (i)<br \/>\n4x + 2y = 0 &#8212;- (ii)<br \/>\nSolve by graphing<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50182\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-40.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 40\" width=\"681\" height=\"649\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-40.jpg 681w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-40-300x286.jpg 300w\" sizes=\"(max-width: 681px) 100vw, 681px\" \/><br \/>\nThe lines are parallel so the system has no solution.<\/p>\n<p>Question 6.<br \/>\n2x &#8211; 4y = 10<br \/>\n-12x + 24y = -60<\/p>\n<p>Answer:<br \/>\nThe system has infinitely many solutions.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n2x &#8211; 4y = 10 &#8212;- (i)<br \/>\n-12x + 24y = -60 &#8212; (ii)<br \/>\nMultiply (i) by 6<br \/>\n6(2x &#8211; 4y = 10)<br \/>\n12x &#8211; 24y = 60 &#8212; (iii)<br \/>\nAdd (ii) &amp; (iii)<br \/>\n-12x + 24y + 12x &#8211; 24y = -60 + 60<br \/>\n0 = 0<br \/>\nSo, the system has infinitely many solutions.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p><strong>STRUCTURE<\/strong><br \/>\n<strong>Without graphing or solving, determine the number of solutions of the system. Explain your reasoning.<\/strong><\/p>\n<p>Question 7.<br \/>\ny = 5x &#8211; 9<br \/>\ny = 5x + 9<\/p>\n<p>Answer:<br \/>\nThe system has infinitely many solutions.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = 5x &#8211; 9<br \/>\ny = 5x + 9<br \/>\nthe slope of the two lines are the same i.e 5<br \/>\nSo, the system has infinitely many solutions.<\/p>\n<p>Question 8.<br \/>\ny = 6x + 2<br \/>\ny = 3x + 1<\/p>\n<p>Answer:<br \/>\nThe system has one solution.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = 6x + 2<br \/>\nslope1 = 6<br \/>\ny = 3x + 1<br \/>\nslope2 = 3<br \/>\nSlopes are different<br \/>\nSo, the system has one solution.<\/p>\n<p>Question 9.<br \/>\ny = 8x &#8211; 2<br \/>\ny &#8211; 8x = -2<\/p>\n<p>Answer:<br \/>\nThe system has infinitely many solutions.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = 8x &#8211; 2<br \/>\nslope 1 = 8<br \/>\ny &#8211; 8x = -2<br \/>\ny = -2 + 8x<br \/>\nslope 2 = 8<br \/>\nthe slope of the two lines are the same i.e 8<br \/>\nSo, the system has infinitely many solutions.<\/p>\n<p><strong>CHOOSING A METHOD<\/strong><br \/>\n<strong>Solve the system. Explain your choice of method.<\/strong><\/p>\n<p>Question 10.<br \/>\n2x + y = 6<br \/>\nx &#8211; y = 3<\/p>\n<p>Answer:<br \/>\nThe solution set is (3, 0).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n2x + y = 6 &#8212;- (i)<br \/>\nx &#8211; y = 3 &#8212; (ii)<br \/>\nAdd equations<br \/>\n2x + y + x &#8211; y = 3 + 6<br \/>\n3x = 9<br \/>\nx = 3<br \/>\nSubstitute x = 3 in (ii)<br \/>\n3 &#8211; y = 3<br \/>\ny = 0<br \/>\nSo, the solution set is (3, 0).<\/p>\n<p>Question 11.<br \/>\n4y &#8211; 4x = 8<br \/>\ny = x + 2<\/p>\n<p>Answer:<br \/>\nThe system has infinitely many solutions.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n4y &#8211; 4x = 8 &#8212; (i)<br \/>\ny = x + 2 &#8212;- (ii)<br \/>\nSubstitute 2 in 1<br \/>\n4(x + 2) &#8211; 4x = 8<br \/>\n4x + 8 &#8211; 4x = 8<br \/>\n8 = 8<br \/>\nSo, the system has infinitely many solutions.<\/p>\n<p>Question 12.<br \/>\n5x &#8211; 4y = 12<br \/>\n7.5x = 6(y &#8211; 1)<\/p>\n<p>Answer:<br \/>\nThe system has no solution.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n5x &#8211; 4y = 12<br \/>\n7.5x = 6(y &#8211; 1)<br \/>\nBy graphing<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50185\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-41.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 41\" width=\"656\" height=\"658\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-41.jpg 656w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-41-300x300.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-41-150x150.jpg 150w\" sizes=\"(max-width: 656px) 100vw, 656px\" \/><br \/>\nThe lines are parrel<br \/>\nSo, the system has no solution.<\/p>\n<p>Question 13.<br \/>\n-6x = 9<br \/>\n6x &#8211; y = 3<\/p>\n<p>Answer:<br \/>\nThe solution set is (-3\/2, -12)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n-6x = 9<br \/>\n6x &#8211; y = 3<br \/>\n-6x = 9<br \/>\nx = -9\/6<br \/>\nx = -3\/2<br \/>\nSubstitute x = -3\/2 in 6x &#8211; y = 3<br \/>\n6(-3\/2) &#8211; y = 3<br \/>\n-18\/2 &#8211; 3 = y<br \/>\ny = -24\/2<br \/>\ny = -12<br \/>\nSo, the solution set is (-3\/2, -12)<\/p>\n<p>Question 14.<br \/>\n0.5x + 4y = -11<br \/>\n-1.5x &#8211; 12y = 33<\/p>\n<p>Answer:<br \/>\nThe system has infinitely many solutions.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n0.5x + 4y = -11<br \/>\n-1.5x &#8211; 12y = 33<br \/>\nBy graphing<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50186\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-42.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 42\" width=\"657\" height=\"657\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-42.jpg 657w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-42-300x300.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-42-150x150.jpg 150w\" sizes=\"(max-width: 657px) 100vw, 657px\" \/><br \/>\nTwo equations are on the same line.<br \/>\nSo, the system has infinitely many solutions.<\/p>\n<p>Question 15.<br \/>\nx = y + 2<br \/>\n3x = 6(y + 2)<\/p>\n<p>Answer:<br \/>\nThe solution set is (0, -2).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\nx = y + 2<br \/>\n3x = 6(y + 2)<br \/>\nBy graphing<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-43.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 43\" width=\"532\" height=\"526\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-43.jpg 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-43-300x297.jpg 300w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><br \/>\nThe point of intersection of two equations is (0, -2)<br \/>\nso, the solution set is (0, -2).<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><\/p>\n<p>Solve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 16.<br \/>\nYour friend wants to sell painted rocks. He spends $10.00 on startup costs, and each painted rock costs him $0.75 to make. A store offers to pay your friend\u2019s startup costs and buy his painted rocks for $0.75 each. How many painted rocks does your friend need to sell to make a pro\ufb01t?<\/p>\n<p>Answer:<br \/>\nNo profit.<\/p>\n<p>Explanation:<br \/>\nThe cost on startup is $10 and each painted rock costs around $0.75 to make<br \/>\nA store pays startup cost and buys his painted rocks for $0.75 each<br \/>\nThere will be no profit because the cost price and selling price is the same. He buys for $0.75 and sells the same for $0.75.<\/p>\n<p>Question 17.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe difference in age of two orangutans is 6 years. In 4 years, is it possible for the older orangutan to be twice as old as the younger orangutan? three times as old? Justify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32593\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-49.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 49\" width=\"189\" height=\"274\" \/><\/p>\n<p>Answer:<br \/>\nBoth are possible<\/p>\n<p>Explanation:<br \/>\nLet us take the age of two orangutans as x and y<br \/>\nThe difference in age of two orangutans is 6 years<br \/>\nx &#8211; y = 6<br \/>\nSo, x is the older one<br \/>\nx = 6 + y<br \/>\nIf the older orangutan to be twice as old as the younger orangutan<br \/>\nx = 2y<br \/>\n2y &#8211; y = 6<br \/>\ny = 6<br \/>\nIf the older orangutan to be three times as old as the younger orangutan<br \/>\nx = 3y<br \/>\n3y &#8211; y = 6<br \/>\n2y = 6<br \/>\ny = 3<br \/>\nBoth are possible, the older orangutan to be twice as old as the younger orangutan when younger age is 6 years and the older orangutan to be three times as old as the younger orangutan when the younger age is 3 years.<\/p>\n<h3><a id=\"Solving_Special_Systems_of_Linear_Equations_Homework_&amp;_Practice_5.4\"><\/a>Solving Special Systems of Linear Equations Homework &amp; Practice 5.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Solve the system by elimination. Check your solution.<\/strong><\/p>\n<p>Question 1.<br \/>\nx + 2y = 4<br \/>\n-x &#8211; y = 2<\/p>\n<p>Answer:<br \/>\nThe solution set is (-8, 6)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\nx + 2y = 4 &#8212; 1<br \/>\n-x &#8211; y = 2 &#8212; 2<br \/>\nAdd both equations<br \/>\nx + 2y &#8211; x &#8211; y = 4 + 2<br \/>\ny = 6<br \/>\nSubstitute y = 6 in 2<br \/>\n-x &#8211; 6 = 2<br \/>\n-x = 2 + 6<br \/>\nx = -8<br \/>\nSubstitute x = -8, y = 6 in 2<br \/>\n8 &#8211; 6 = 2<br \/>\nSo, the solution set is (-8, 6)<\/p>\n<p>Question 2.<br \/>\n2x &#8211; y = 1<br \/>\nx + 3y &#8211; 4 = 0<\/p>\n<p>Answer:<br \/>\nThe solution set is (1, 1).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n2x &#8211; y = 1 &#8212;- (i)<br \/>\nx + 3y &#8211; 4 = 0 &#8212;- (ii)<br \/>\nMultiply (i) by 3<br \/>\n3(2x &#8211; y = 1)<br \/>\n6x &#8211; 3y = 3 &#8212;- (iii)<br \/>\nAdd (iii) &amp; (ii)<br \/>\n6x &#8211; 3y + x + 3y &#8211; 4 = 3<br \/>\n7x = 3 + 4<br \/>\n7x = 7<br \/>\nx = 1<br \/>\nSubstitute x = 1 in (i)<br \/>\n2(1) &#8211; y = 1<br \/>\n2 &#8211; y = 1<br \/>\n2 &#8211; 1 = y<br \/>\ny = 1<br \/>\nSubstitute x = 1, y = 1 in (i)<br \/>\n2(1) &#8211; 1 = 2 &#8211; 1 = 1<br \/>\nSo, the solution set is (1, 1).<\/p>\n<p>Question 3.<br \/>\n3x = -4y + 10<br \/>\n4x + 3y = 11<\/p>\n<p>Answer:<br \/>\nThe solution set is (2, 1).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n3x = -4y + 10<br \/>\n3x + 4y = 10 &#8212;- (i)<br \/>\n4x + 3y = 11&#8212;- (ii)<br \/>\nMultiply (i) by 4 and (ii) by 3<br \/>\n4(3x + 4y = 10)<br \/>\n12x + 16y = 40 &#8212;- (iii)<br \/>\n3(4x + 3y = 11)<br \/>\n12x + 9y = 33 &#8212;- (iv)<br \/>\nSubtract (iii) from (iv)<br \/>\n12x + 16y &#8211; 12x &#8211; 9y = 40 &#8211; 33<br \/>\n7y = 7<br \/>\ny = 1<br \/>\nSubstitute y = 1 in (i)<br \/>\n3x + 4 = 10<br \/>\n3x = 6<br \/>\nx = 2<br \/>\nSubstitute x = 2, y = 1 in (i)<br \/>\n3(2) + 4 = 6 + 4 = 10<br \/>\nSo, the solution set is (2, 1).<\/p>\n<p><strong>Write an equation of the line that passes through the given points.<\/strong><\/p>\n<p>Question 4.<br \/>\n(0, 0), (2, 6)<\/p>\n<p>Answer:<br \/>\ny = 3x<\/p>\n<p>Explanation:<br \/>\nThe equation of a line when two points given is<br \/>\n(y \u2013 y\u2081) = [(y\u2082 \u2013 y\u2081)\/(x\u2082 \u2013 x\u2081)](x \u2013 x\u2081)<br \/>\nx\u2081 = 0, y\u2081 = 0, x\u2082 = 2, y\u2082 = 6<br \/>\nSo, (y &#8211; 0) = [(6 &#8211; 0)\/(2 &#8211; 0)] (x &#8211; 0)<br \/>\ny = 3x<\/p>\n<p>Question 5.<br \/>\n(0, -3), (3, 3)<\/p>\n<p>Answer:<br \/>\ny = 2x &#8211; 3<\/p>\n<p>Explanation:<br \/>\nThe equation of a line when two points given is<br \/>\n(y \u2013 y\u2081) = [(y\u2082 \u2013 y\u2081)\/(x\u2082 \u2013 x\u2081)](x \u2013 x\u2081)<br \/>\nx\u2081 = 0, y\u2081 = -3, x\u2082 = 3, y\u2082 = 3<br \/>\nSo, (y + 3) = [(3 + 3)\/(3 &#8211; 0)](x &#8211; 0)<br \/>\n(y + 3)\u00a0 = 2x<br \/>\ny = 2x &#8211; 3<\/p>\n<p>Question 6.<br \/>\n(-6, 5), (0, 2)<\/p>\n<p>Answer:<br \/>\nx + 2y = 6<\/p>\n<p>Explanation:<br \/>\nThe equation of a line when two points are given is<br \/>\n(y \u2013 y\u2081) = [(y\u2082 \u2013 y\u2081)\/(x\u2082 \u2013 x\u2081)](x \u2013 x\u2081)<br \/>\nx\u2081 = -6, y\u2081 = 5, x\u2082 = 0, y\u2082 = 2<br \/>\nSo, (y &#8211; 5) = [(2 &#8211; 5)\/(0 + 6)](x + 6)<br \/>\ny &#8211; 6 = -3\/6 (x + 6)<br \/>\ny &#8211; 6 = -1\/2 (x + 6)<br \/>\n2(y &#8211; 6) = -1(x + 6)<br \/>\n2y &#8211; 12 = -x &#8211; 6<br \/>\n2y = -x &#8211; 6 + 12<br \/>\nx + 2y = 6<\/p>\n<p><strong>Concepts, Skills, &amp;Problem Solving<\/strong><br \/>\n<strong>EXPLORING SOLUTIONS OF SYSTEMS<\/strong><br \/>\n<strong>Use a graph to determine the number of solutions of the system.<\/strong> (See Exploration 1, p. 219.)<\/p>\n<p>Question 7.<br \/>\ny = 2x + 1<br \/>\ny = 2x + 5<\/p>\n<p>Answer:<br \/>\nThe system has no solution.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = 2x + 1, y = 2x + 5<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50194\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-44.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 44\" width=\"671\" height=\"654\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-44.jpg 671w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-44-300x292.jpg 300w\" sizes=\"(max-width: 671px) 100vw, 671px\" \/><br \/>\nThe lines are parallel<br \/>\nSo, the system has no solution.<\/p>\n<p>Question 8.<br \/>\ny + 8 = 0<br \/>\ny = 8<\/p>\n<p>Answer:<br \/>\nThe system has no solution.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y + 8 = 0, y = 8<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50195\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-45.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 45\" width=\"682\" height=\"651\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-45.jpg 682w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-45-300x286.jpg 300w\" sizes=\"(max-width: 682px) 100vw, 682px\" \/><br \/>\nThe lines are parallel<br \/>\nSo, the system has no solution.<\/p>\n<p>Question 9.<br \/>\nx + y = 2<br \/>\n5x + y = 9<\/p>\n<p>Answer:<br \/>\nThe solution is (7\/4, 1\/4)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are x + y = 2, 5x + y = 9<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50196\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-46.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 46\" width=\"531\" height=\"536\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-46.jpg 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-46-297x300.jpg 297w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-46-150x150.jpg 150w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><br \/>\nThe lines intersect at (7\/4, 1\/4)<br \/>\nSo, the solution is (7\/4, 1\/4)<\/p>\n<p><strong>SOLVING A SYSTEM<\/strong><br \/>\n<strong>Solve the system. Explain your choice of method.<\/strong><\/p>\n<p>Question 10.<br \/>\ny = 2x &#8211; 2<br \/>\ny = 2x + 9<\/p>\n<p>Answer:<br \/>\nThe system has no solution.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = 2x &#8211; 2 &#8212; (i)<br \/>\ny = 2x + 9 &#8212; (ii)<br \/>\nEquate equations<br \/>\n2x &#8211; 2 = 2x + 9<br \/>\nSo, the system has no solution.<\/p>\n<p>Question 11.<br \/>\ny = 3x + 1<br \/>\n-x + 2y = -3<\/p>\n<p>Answer:<br \/>\nThe solution is (-1, -2).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = 3x + 1, -x + 2y = -3<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50198\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-47.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 47\" width=\"525\" height=\"516\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-47.jpg 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-47-300x295.jpg 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><br \/>\nThe lines intersect at (-1, -2)<br \/>\nSo, the solution is (-1, -2).<\/p>\n<p>Question 12.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32594\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-50.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 50\" width=\"138\" height=\"67\" \/><\/p>\n<p>Answer:<br \/>\nThe system has no solution.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = \u03c0\/3 x + \u03c0 &#8212;- (i)<br \/>\n-\u03c0x + 3y = -6\u03c0 &#8212;- (ii)<br \/>\nSubstitute (i) in (ii)<br \/>\n-\u03c0x + 3(\u03c0\/3 x + \u03c0) = -6\u03c0<br \/>\n-\u03c0x + \u03c0x + 3\u03c0 = -6\u03c0<br \/>\nSo, the system has no solution.<\/p>\n<p>Question 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32595\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-51.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 51\" width=\"109\" height=\"67\" \/><\/p>\n<p>Answer:<br \/>\nThe system has infinitely many solutions.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = -1\/6 x + 5 &#8212;-(i)<br \/>\nx + 6y = 30 &#8212;- (ii)<br \/>\nSubstitute (i) in (ii)<br \/>\nx + 6(-1\/6 x + 5) = 30<br \/>\nx &#8211; x + 30 = 30<br \/>\nSo, the system has infinitely many solutions.<\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32596\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-52.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 52\" width=\"102\" height=\"66\" \/><\/p>\n<p>Answer:<br \/>\nThe system has infinitely many solutions.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\n1\/3 x + y = 1 &#8212;- (i)<br \/>\n2x + 6y = 6 &#8212;- (ii)<br \/>\nDivide (ii) by 1\/6<br \/>\n1\/6(2x + 6y = 6)<br \/>\n1\/3 x + y = 1 &#8212;- (iii)<br \/>\nequation (i) &amp; (iii) are same<br \/>\nSo, the system has infinitely many solutions.<\/p>\n<p>Question 15.<br \/>\n-2x + y = 1.3<br \/>\n2(0.5x &#8211; y) = 4.6<\/p>\n<p>Answer:<br \/>\nThe solution is (-2.4, -3.5)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are -2x + y = 1.3, 2(0.5x &#8211; y) = 4.6<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-48.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 48\" width=\"539\" height=\"523\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-48.jpg 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-48-300x291.jpg 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><br \/>\nThe lines intersect at (-2.4, -3.5)<br \/>\nSo, the solution is (-2.4, -3.5)<\/p>\n<p>Question 16.<br \/>\n2(x + y) = 9<br \/>\n1 = -4(x + y)<\/p>\n<p>Answer:<br \/>\nThe system has no solution.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are 2(x + y) = 9, 1 = -4(x + y)<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50202\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-49.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 49\" width=\"674\" height=\"647\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-49.jpg 674w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-49-300x288.jpg 300w\" sizes=\"(max-width: 674px) 100vw, 674px\" \/><br \/>\nThe lines are parallel<br \/>\nSo, the system has no solution.<\/p>\n<p>Question 17.<br \/>\ny = 9x<br \/>\nx + y = 1<\/p>\n<p>Answer:<br \/>\nThe solution is (1\/10, 9\/10)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = 9x, x + y = 1<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50203\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-50.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 50\" width=\"533\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-50.jpg 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-50-300x294.jpg 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><br \/>\nThe lines intersect at (1\/10, 9\/10)<br \/>\nSo, the solution is (1\/10, 9\/10)<\/p>\n<p>Question 18.<br \/>\n0.2y = 4.6x + 1.2<br \/>\n-2.3x = -0.1y + 0.6<\/p>\n<p>Answer:<br \/>\nThe system has infinitely many solutions<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are 0.2y = 4.6x + 1.2, -2.3x = -0.1y + 0.6<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50204\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-51.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 51\" width=\"670\" height=\"650\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-51.jpg 670w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-51-300x291.jpg 300w\" sizes=\"(max-width: 670px) 100vw, 670px\" \/><br \/>\nTwo equations lies on the same line<br \/>\nSo, the system has infinitely many solutions<\/p>\n<p>Question 19.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend \ufb01nds the number of solutions of the system. Is your friend correct? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32597\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-53.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 53\" width=\"267\" height=\"128\" \/><\/p>\n<p>Answer:<br \/>\nCorrect.<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are<br \/>\ny = -2x + 4<br \/>\ny = -2x + 6<br \/>\nTwo equations have the same slope<br \/>\nSo, the system has infinitely many solutions.<\/p>\n<p>Question 20.<br \/>\n<strong>REASONING<\/strong><br \/>\nIn a pig race, your pig has a head start of 3 feet and runs at a rate of 2 feet per second. Your friend\u2019s pig also runs at a rate of 2 feet per second. A system of linear equations that represents this situation is y = 2x + 3 and y = 2x. Does your friend\u2019s pig catch up to your pig? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32598\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-54.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 54\" width=\"352\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-54.png 352w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-54-300x207.png 300w\" sizes=\"(max-width: 352px) 100vw, 352px\" \/><\/p>\n<p>Answer:<br \/>\nNo.<\/p>\n<p>Explanation:<br \/>\ny = 2x + 3 and y = 2x<br \/>\nSubstitute y = 2x in y = 2x + 3<br \/>\n2x = 2x + 3<br \/>\n2x &#8211; 2x = 3<br \/>\n0 = 3<br \/>\nThe system has no solution<br \/>\nYour friend\u2019s pig never catch up to your pig<\/p>\n<p>Question 21.<br \/>\n<strong>REASONING<\/strong><br \/>\nOne equation in a system of linear equations has a slope of 3. The other equation has a slope of 4. How many solutions does the system have? Explain.<\/p>\n<p>Answer:<br \/>\nThe system has one solution.<\/p>\n<p>Explanation:<br \/>\nOne equation in a system of linear equations has a slope of 3. The other equation has a slope of 4<br \/>\nAs the slopes are different. The system has one solution.<\/p>\n<p>Question 22.<br \/>\n<strong>LOGIC<\/strong><br \/>\nHow can you use the slopes and the y-intercepts of equations in a system one solution, in\ufb01nitely many solutions, or no solution?<\/p>\n<p>Answer:<br \/>\nThe slope-intercept form of a line is y = mx + c<br \/>\nIf the slope is the same, different y-intercept for the two equations, then the system has no solution.<br \/>\nIf the slope is different for two equations, then the system has one solution.<br \/>\nIf the slope is the same, the same y-intercept for two equations, then the system has infinitely many solutions.<\/p>\n<p>Question 23.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou and a friend both work two different jobs. The system of linear equations represents the total earnings (in dollars) for x hours worked at the \ufb01rst job and y hours worked at the second job. Your friend earns twice as much as you.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32599\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-55.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 55\" width=\"242\" height=\"54\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32600\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-56.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 56\" width=\"169\" height=\"110\" \/><br \/>\na. One week, both of you work 4 hours at the \ufb01rst job. How many hours do you and your friend work at the second job?<br \/>\nb. Both of you work the same number of hours at the second job. Compare the number of hours you and your friend work at the \ufb01rst job.<\/p>\n<p>Answer:<br \/>\na. 16 hours you and your friend work at the second job<br \/>\nb. If both work the same y hours at a second job, then both will same x hours at the first job.<\/p>\n<p>Explanation:<br \/>\nLet x represent the first job and y represents the second job<br \/>\nThe system of linear equations for the total number of hours for the first job &amp; second job for you &amp; your friend is<br \/>\n4x + 8y = 64<br \/>\n8x + 16y = 128<br \/>\na. If x = 4<br \/>\n8(4) + 16y = 128<br \/>\n32 + 16y = 128<br \/>\n16y = 128 &#8211; 32<br \/>\n16y = 96<br \/>\ny = 16 hours<br \/>\nb. If both work the same y hours at the second job, then both will same x hours at the first job.<\/p>\n<p>Question 24.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou download a digital album for $10.00. Then you and your friend each download the same number of individual songs for $0.99 each. Write a system of linear equations that represents this situation. Will you and your friend spend the same amount of money? Explain.<\/p>\n<p>Answer:<br \/>\nNo<\/p>\n<p>Explanation:<br \/>\nWrite the equations for you and your friends&#8217; total cost y where x is the number of songs<br \/>\nyou y = 10 + 0.99x<br \/>\nyour friend y = 0.99x<br \/>\nThe two equations have the same slope but different y-intercepts so the system has no solution.<\/p>\n<p>Question 25.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nThe table shows the research activities of two students at an observatory. How much does a student pay to use the telescope for one hour?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32601\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-57.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 57\" width=\"496\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-57.png 496w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-57-300x70.png 300w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><\/p>\n<p>Answer:<br \/>\nA student must pay $7.5 for using a telephone per hour and $11 for using a supercomputer per hour.<\/p>\n<p>Explanation:<br \/>\nLet the cost of telephonic use be x, supercomputer use be y. The system of equations are<br \/>\n5x + 3y = 70.50 &#8212; (i)<br \/>\n6x + 2y = 67 &#8212;- (ii)<br \/>\nMultiply (i) by 2 and (ii) by 3 and subtract them<br \/>\n10x + 6y = 141<br \/>\n18x + 6y = 201<br \/>\n10x + 6y &#8211; 18x &#8211; 6y = 141 &#8211; 201<br \/>\n-8x = -60<br \/>\nx = 7.5<br \/>\nSubstitute x = 7.5 in (ii)<br \/>\n6(7.5) + 2y = 67<br \/>\n45 + 2y = 67<br \/>\n2y = 67 &#8211; 45<br \/>\n2y = 22<br \/>\ny = 11<br \/>\nSo, a student must pay $7.5 for using telephone per hour and $11 for using supercomputer per hour.<\/p>\n<p>Question 26.<br \/>\n<strong>REASONING<\/strong><br \/>\nDoes the system shown always, sometimes, or never have a solution when a = b? a \u2265 b? a &lt; b? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32602\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-58.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 58\" width=\"109\" height=\"75\" \/><\/p>\n<p>Answer:<br \/>\nIf a = b, the system will always have no solution<br \/>\nIf a \u2265 b, the system will sometimes have no solution.<br \/>\nIf a &lt; b, the system will never have no solution.<\/p>\n<p>Explanation:<br \/>\nIf a = b, then two linear equations will have the same slope but different y-intercepts. So, they will always have no solution<br \/>\nIf a \u2265 b, then the slopes may be different or the same so they may intersect once or not at all. Therefore, they will sometimes have no solution.<br \/>\nIf a &lt; b, then the equations have a different slope so they will intersect once. so, they will never have no solution.<\/p>\n<p>Question 27.<br \/>\n<strong>LOGIC<\/strong><br \/>\nThe table shows the numbers of lift tickets and ski rentals sold to different groups. Is it possible to determine how much each lift ticket costs using the information for Groups 1 and 2? Groups 1 and 3? Justify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32603\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-89.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 89\" width=\"266\" height=\"173\" \/><\/p>\n<p>Answer:<br \/>\na. It is not possible to find out the cost of lift tickets using the given information.<br \/>\nb. The cost of a lift ticket is $14, cost of ski rental is $10.<\/p>\n<p>Explanation:<br \/>\nLet the cost for lift tickets and cost for sky rentals be y. The system of equations are<br \/>\n36x + 18y = 684 &#8212; (i)<br \/>\n24x + 12y = 456 &#8212;- (ii)<br \/>\n18x + 18y = 432 &#8212;-(iii)<br \/>\n3(12x + 6y) = 684<br \/>\n12x + 6y = 228<br \/>\n2(12x + 6y) = 456<br \/>\n12x + 6y = 228<br \/>\nBoth the equations are same. So, they have infinately many solutions.<br \/>\nHence, it is not possible to find out the cost of lift tickets using the given information.<br \/>\nb. Subtract 1 from 2<br \/>\n36x + 18y &#8211; 18x &#8211; 18y = 684 &#8211; 432<br \/>\n18x = 252<br \/>\nx = 14<br \/>\nPut x = 14<br \/>\n36(14) + 18y = 684<br \/>\n504 + 18y = 684<br \/>\n18y = 180<br \/>\ny = 10<br \/>\nThe cost of lift ticket is $14, cost of ski rentaks is $10.<\/p>\n<p>Question 28.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nFind the values of a and b so the system is shown has the solution (2, 3). Does the system have any other solutions for these values of a and b? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32604\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-90.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 90\" width=\"149\" height=\"82\" \/><\/p>\n<p>Answer:<br \/>\n(a, b) = (2, 2)<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\n12x &#8211; 2by = 12<br \/>\n3ax &#8211; by = 6<br \/>\nThe value of a, b if (x, y) = (2, 3)<br \/>\n12(2) &#8211; 2b(3) = 12<br \/>\n24 &#8211; 6b = 12<br \/>\n6b = 24 &#8211; 12<br \/>\n6b = 12<br \/>\nb = 2<br \/>\n3a(2) &#8211; 3b = 6<br \/>\n6a &#8211; 3(2) = 6<br \/>\n6a &#8211; 6 = 6<br \/>\n6a = 12<br \/>\na = 2<br \/>\nThe system of equations are<br \/>\n12x &#8211; 4y = 12<br \/>\n2(6x &#8211; 2y) = 12<br \/>\n6x &#8211; 2y = 6 &#8212; (i)<br \/>\n6x &#8211; 2y = 6 &#8212; (ii)<br \/>\nAs both the equations are same, they have infinately many solutions<br \/>\n(a, b) = (2, 2)<\/p>\n<h3><a id=\"Systems_of_Linear_Equations_Connecting_Concepts\"><\/a>Systems of Linear Equations Connecting Concepts<\/h3>\n<p><strong>Connecting Concepts<\/strong><\/p>\n<p><strong>Using the Problem-Solving Plan<\/strong><\/p>\n<p>Question 1.<br \/>\nAn animal shelter has a total of 65 cats and dogs. The ratio of cats to dogs is 6:7. Find the number of cats and the number of dogs in the shelter.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32605\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-91.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 91\" width=\"189\" height=\"198\" \/><br \/>\n<strong>Understand the problem.<\/strong><br \/>\nYou know the total number of cats and dogs in an animal shelter, and the ratio of cats to dogs. You are asked to \ufb01nd the number of cats and the number of dogs in the shelter.<br \/>\n<strong>Make a plan.<\/strong><br \/>\nWrite a system of equations. Use the total number of cats and dogs to write an equation relating the number of cats and the number of dogs. Use the ratio of cats to dogs to write a second equation. Then solve the system.<br \/>\n<strong>Solve and check.<\/strong><br \/>\nUse the plan to solve the problem. Then check your solution.<\/p>\n<p>Answer:<br \/>\nThe number of cats in the shelter is 30, the number of dogs are 35.<\/p>\n<p>Explanation:<br \/>\nLet us take the number of dogs as x, cats as y<br \/>\nAn animal shelter has a total of 65 cats and dogs.<br \/>\nx + y = 65 &#8212; (i)<br \/>\nThe ratio of cats to dogs is 6:7<br \/>\nx : y = 6 : 7<br \/>\n6x = 7y<br \/>\nx = 7y\/6<br \/>\nSubstitute x = 7y\/6 in (i)<br \/>\n7y\/6 + y = 65<br \/>\n7y + 6y = 65(6)<br \/>\n13y = 390<br \/>\ny = 30<br \/>\nSubstitute y = 30 in (i)<br \/>\nx + 30 = 65<br \/>\nx = 65 &#8211; 30<br \/>\nx = 35<br \/>\nSo, the number of cats in the shelter are 30, number of dogs are 35.<\/p>\n<p>Question 2.<br \/>\nThe measure of \u22201 is 15 degrees less than two times the measure of \u22202. Find the measure of each of the four angles formed by the intersecting lines. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32606\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-92.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 92\" width=\"150\" height=\"118\" \/><\/p>\n<p>Answer:<br \/>\nThe angles are \u22201 = 125, \u22202 = 55, \u22203 = 125, \u22204 = 55.<\/p>\n<p>Explanation:<br \/>\nThe measure of \u22201 is 15 degrees less than two times the measure of \u22202.<br \/>\n\u22201 &#8211; 15 = 2(\u22202) &#8212; (i)<br \/>\n\u22201 + \u22202 = 180 degrees &#8212; (ii)<br \/>\n\u22201 = 180 &#8211; \u22202<br \/>\n180 &#8211; \u22202 &#8211; 15 = 2(\u22202)<br \/>\n165 = 2\u22202 + \u22202<br \/>\n165 = 3\u22202<br \/>\n\u22202 = 55 degrees<br \/>\nSubstitute \u22202 = 55 in (i)<br \/>\n\u22201 &#8211; 15 = 2(55)<br \/>\n\u22201 = 110 + 15<br \/>\n\u22201 = 125 degrees<br \/>\nSo, the angles are \u22201 = 125, \u22202 = 55, \u22203 = 125, \u22204 = 55.<\/p>\n<p>Question 3.<br \/>\nA landscaper plants grass seed over the entire area of two parks that are similar in shape. The ratio of the perimeter of Park A to the perimeter of Park B is 2 : 1. The parks have a combined area of 9000 square feet. How many square feet does the landscaper cover with grass seed at ParkA? Park B? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32607\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-93.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 93\" width=\"217\" height=\"184\" \/><\/p>\n<p>Answer:<br \/>\nThe landscaper cover with grass seed at ParkA is 60\u221a2 at park B is 30\u221a2.<\/p>\n<p>Explanation:<br \/>\nlet the side of park A is x, park b is y.<br \/>\nThe ratio of the perimeter of Park A to the perimeter of Park B is 2 : 1<br \/>\nx : y = 2 : 1<br \/>\nx = 2y &#8212; (i)<br \/>\nThe parks have a combined area of 9000 square feet<br \/>\nx\u00b2 + y\u00b2 = 9000 &#8212;- (ii)<br \/>\nSubstitute x = 2y in (ii)<br \/>\n(2y)\u00b2 + y\u00b2 = 9000<br \/>\n4y\u00b2 + y\u00b2 = 9000<br \/>\n5y\u00b2 = 9000<br \/>\ny\u00b2 = 1800<br \/>\ny = 30\u221a2<br \/>\nSubstitute y = 30\u221a2 in (i)<br \/>\nx = 2(30\u221a2)<br \/>\n= 60\u221a2<br \/>\nThe landscaper cover with grass seed at ParkA is 60\u221a2 at park B is 30\u221a2.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p><strong>Mixing Alloys<\/strong><\/p>\n<p>At the beginning of this chapter, you watched a STEAM Video called \u201cGold Alloys.\u201d You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32612\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-94.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 94\" width=\"281\" height=\"199\" \/><\/p>\n<h3><a id=\"Systems_of_Linear_Equations_Chapter_Review\"><\/a>Systems of Linear Equations Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the de\ufb01nition and give an example of each vocabulary term.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32608\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-95.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 95\" width=\"634\" height=\"34\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-95.png 634w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-95-300x16.png 300w\" sizes=\"(max-width: 634px) 100vw, 634px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><\/p>\n<p>You can use a Four Square to organize information about a concept. Each of the four squares can be a category, such as de\ufb01nition, vocabulary, example, non-example, words, algebra, table, numbers, visual, graph, or equation. Here is an example of a Four Square for solving systems of linear equations by graphing.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32609\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-96.png\" alt=\"Big Ideas Math Answers 8th Grade Chapter 5 Systems of Linear Equations 96\" width=\"552\" height=\"378\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-96.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-8th-Grade-Chapter-5-Systems-of-Linear-Equations-96-300x205.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p><strong>Choose and complete a graphic organizer to help you study the concept.<\/strong><\/p>\n<ol>\n<li>solving systems of linear equations by substitution<\/li>\n<li>solving systems of linear equations by elimination<\/li>\n<li>systems of linear equations with no solution<\/li>\n<li>systems of linear equations with in\ufb01nitely many solutions<\/li>\n<\/ol>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32613\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-97.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 97\" width=\"281\" height=\"354\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-97.png 281w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-97-238x300.png 238w\" sizes=\"(max-width: 281px) 100vw, 281px\" \/><\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32614\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-98.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 98\" width=\"641\" height=\"78\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-98.png 641w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-98-300x37.png 300w\" sizes=\"(max-width: 641px) 100vw, 641px\" \/><\/p>\n<p><strong>5.1 Solving Systems of Linear Equations by Graphing<\/strong> (pp. 199-204)<\/p>\n<p><strong>Solve the system by graphing.<\/strong><\/p>\n<p>Question 1.<br \/>\ny = 2x &#8211; 3<br \/>\ny = x + 2<\/p>\n<p>Answer:<br \/>\nThe solution is (5, 7)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = 2x &#8211; 3, y = x + 2<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49552\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-224.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 24\" width=\"542\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-224.jpg 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-224-300x289.jpg 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><br \/>\nThe lines intersect at (5, 7)<br \/>\nSo, the solution is (5, 7)<\/p>\n<p>Question 2.<br \/>\ny = -x + 4<br \/>\nx + 2y = 0<\/p>\n<p>Answer:<br \/>\nThe solution is (8, -4)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = -x + 4, x + 2y = 0<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49553\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-25.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 25\" width=\"529\" height=\"525\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-25.jpg 529w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-25-300x298.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-25-150x150.jpg 150w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><br \/>\nThe lines intersect at (8, -4)<br \/>\nSo, the solution is (8, -4)<\/p>\n<p>Question 3.<br \/>\nx &#8211; y = -2<br \/>\n2x &#8211; 3y = -2<\/p>\n<p>Answer:<br \/>\nThe solution is (-4, -2).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are x &#8211; y = -2, 2x &#8211; 3y = -2<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49554\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-26.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 26\" width=\"527\" height=\"533\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-26.jpg 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-26-297x300.jpg 297w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><br \/>\nThe lines intersect at (-4, -2)<br \/>\nSo, the solution is (-4, -2)<\/p>\n<p><strong>Use a graphing calculator to solve the system.<\/strong><\/p>\n<p>Question 4.<br \/>\ny = -0.5x<br \/>\ny = 0.75x + 1.25<\/p>\n<p>Answer:<br \/>\nThe solution is (-1, 0.5)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = -0.5x, y = 0.75x + 1.25<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49555\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-27.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 27\" width=\"539\" height=\"530\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-27.jpg 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-27-300x295.jpg 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><br \/>\nThe lines intersect at (-1, 0.5)<br \/>\nSo, the solution is (-1, 0.5)<\/p>\n<p>Question 5.<br \/>\ny = 0.2x &#8211; 3<br \/>\n10x + 3y = 5<\/p>\n<p>Answer:<br \/>\nThe solution is (1.3, -2.7)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = 0.2x &#8211; 3, 10x + 3y = 5<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49556\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-28.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 28\" width=\"535\" height=\"540\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-28.jpg 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-28-297x300.jpg 297w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-28-150x150.jpg 150w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><br \/>\nThe lines intersect at (1.3, -2.7)<br \/>\nSo, the solution is (1.3, -2.7)<\/p>\n<p>Question 6.<br \/>\n2.6x + 1.3y = 7.8<br \/>\n1.2x &#8211; 3.6y = 12<\/p>\n<p>Answer:<br \/>\nThe solution is (4, -2)<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are 2.6x + 1.3y = 7.8, 1.2x &#8211; 3.6y = 12<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49558\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-29.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 29\" width=\"530\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-29.jpg 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-29-300x297.jpg 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><br \/>\nThe lines intersect at (4, -2)<br \/>\nSo, the solution is (4, -2)<\/p>\n<p>Question 7.<br \/>\nThe sum of the two numbers is 38. Find each number when one number is 8 more than the other number. Use a system of linear equations to justify your answer.<\/p>\n<p>Answer:<br \/>\nThe numbers are 15, 28.<\/p>\n<p>Explanation:<br \/>\nLet the two numbers be x, y<br \/>\nThe sum of two numbers is 38<br \/>\nx + y = 38 &#8212; (i)<br \/>\nOne number is 8 more than the other number<br \/>\nx + 8 = y &#8212; (ii)<br \/>\nSubstitute y = x + 8 in (i)<br \/>\nx + x + 8\u00a0 = 38<br \/>\n2x + 8 = 38<br \/>\n2x = 38 &#8211; 8<br \/>\n2x = 30<br \/>\nx = 15<br \/>\nSubstitute x = 15 in (ii)<br \/>\ny = 15 + 8<br \/>\ny = 23<br \/>\nSo, the numbers are 15, 28.<\/p>\n<p>Question 8.<br \/>\nYou observe the heights of two plants for an experiment. Plant A has a height of 8 centimeters and grows 1 centimeter each week. Plant B has a height of 4 centimeters and grows 2 centimeters each week.<br \/>\na. Write a system of linear equations that represents this situation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32615\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-99.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 99\" width=\"304\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-99.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-99-300x208.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nb. Will the plants ever have the same height? If so, what is the height?<\/p>\n<p>Answer:<br \/>\na. y = x + 8, y = 2x + 4<br \/>\nb. The same height will be 12 cm after4 weeks.<\/p>\n<p>Explanation:<br \/>\nLet the total height be y, growth of the plant each week be x.<br \/>\nPlant A has a height of 8 centimeters and grows 1 centimeter each week. Plant B has a height of 4 centimeters and grows 2 centimeters each week.<br \/>\na. y = x + 8 &#8212; (i)<br \/>\ny = 2x + 4 &#8212;- (ii)<br \/>\nb. If plants ever have the same height<br \/>\nx + 8 = 2x + 4<br \/>\n2x &#8211; x = 8 &#8211; 4<br \/>\nx = 4<br \/>\ny = 4 + 8<br \/>\ny = 12<br \/>\nThe same height will be 12 cm after4 weeks.<\/p>\n<p>Question 9.<br \/>\nWrite a system of linear equations containing the equation y = -3x + 2 and that has a solution of (-1, 5). Use a graph to justify your answer.<\/p>\n<p>Answer:<br \/>\nThe equation is y = x + 6<\/p>\n<p>Explanation:<br \/>\nEquation is y = -3x + 2<br \/>\nThe point is (-1, 5)<br \/>\nThe slope intercept form is y = mx + c<br \/>\n5 = -m + c<br \/>\nIf m = 1<br \/>\nthen c = 5 = -1 + c<br \/>\nc = 6<br \/>\nThen the equation is y = x + 6<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-50280 size-medium\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-52-300x296.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 52\" width=\"300\" height=\"296\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-52-300x296.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-52.jpg 661w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>5.2 Solving Systems of Linear Equations by Substitution<\/strong> (pp. 205\u2013210)<\/p>\n<p><strong>Solve the system by substitution. Check your solution.<\/strong><\/p>\n<p>Question 10.<br \/>\ny = -3x &#8211; 7<br \/>\ny = x + 9<\/p>\n<p>Answer:<br \/>\nThe solution set is (-4, 5).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\ny = -3x &#8211; 7 &#8212;- (i)<br \/>\ny = x + 9 &#8212;- (ii)<br \/>\nSubstitute (i) in (ii)<br \/>\n-3x &#8211; 7 = x + 9<br \/>\n-3x &#8211; x = 9 + 7<br \/>\n-4x = 16<br \/>\nx = -4<br \/>\nSubstitute x = -4 in (i)<br \/>\ny = -3(-4) &#8211; 7<br \/>\ny = 12 &#8211; 7<br \/>\ny = 5<br \/>\nSubstitute x = -4, y = 5 in (i)<br \/>\n5 = -3(-4) &#8211; 7 = 12 &#8211; 7<br \/>\nSo, the solution set is (-4, 5).<\/p>\n<p>Question 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32616\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-100.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 100\" width=\"106\" height=\"76\" \/><\/p>\n<p>Answer:<br \/>\nThe solution set is (-8, 0)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n1\/2 x + y = -4 &#8212;- (i)<br \/>\ny = 2x + 16 &#8212;-(ii)<br \/>\nSubstitute (ii) in (i)<br \/>\n1\/2 x + 2x + 16 = -4<br \/>\n2.5x = -4 &#8211; 16<br \/>\n2.5x = -20<br \/>\nx = -8<br \/>\nSubstitute x = -8 in (ii)<br \/>\ny = 2(-8) + 16<br \/>\ny = -16 + 16<br \/>\ny = 0<br \/>\nSubstitute x = -8, y = 0 in (ii)<br \/>\n0 = 2(-8) + 16 = -16 + 16<br \/>\nSo, the solution set is (-8, 0)<\/p>\n<p>Question 12.<br \/>\n-x + 5y = 28<br \/>\nx + 3y = 20<\/p>\n<p>Answer:<br \/>\nThe solution set is (2, 6)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n-x + 5y = 28<br \/>\nx + 3y = 20 &#8212;- (ii)<br \/>\nx = 5y &#8211; 28 &#8212;- (i)<br \/>\nSubstitute (i) in (ii)<br \/>\n5y &#8211; 28 + 3y = 20<br \/>\n8y &#8211; 28 = 20<br \/>\n8y = 48<br \/>\ny = 6<br \/>\nSubstitute y = 6 in (i)<br \/>\nx = 5(6) &#8211; 28<br \/>\n= 30 &#8211; 28<br \/>\nx = 2<br \/>\nSubstitute y = 6, x = 2 in (ii)<br \/>\n2 + 3(6) = 2 + 18 = 20<br \/>\nSo, the solution set is (2, 6)<\/p>\n<p>Question 13.<br \/>\nZoo admission costs $6 for children and $9 for adults. On Monday, 2200 people visit the zoo and the zoo collects $14,850 in admissions.<br \/>\na. Write a system of linear equations that represents this situation.<br \/>\nb. How many zoo visitors are children? adults?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32617\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-101.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 101\" width=\"289\" height=\"196\" \/><\/p>\n<p>Answer:<br \/>\na. 6x + 9y = 14850, x + y = 2200<br \/>\nb. There are 1650 child visitors and 550 adult visitors.<\/p>\n<p>Explanation:<br \/>\nThe cost for the zoo is $6 for children &amp; $9 for adults. On Monday, 2200 people visit the zoo and the zoo collects $14,850 in admissions.<br \/>\na. The system of equations are<br \/>\n6x + 9y = 14850 &#8212; (i)<br \/>\nx + y = 2200 &#8212; (ii)<br \/>\nb. Multiply (ii) by 6<br \/>\n6x + 6y = 13200<br \/>\n6x + 6y &#8211; 6x &#8211; 9y = 13200 &#8211; 14850<br \/>\n-3y = -1650<br \/>\ny = 550<br \/>\nSubstitute y = 550 in (ii)<br \/>\nx + 550 = 2200<br \/>\nx = 2200 &#8211; 550<br \/>\nx = 1650<br \/>\nThere are 1650 child visitors and 550 adult visitors.<\/p>\n<p><strong>Solve the system. Explain your choice of method.<\/strong><\/p>\n<p>Question 14.<br \/>\ny = x &#8211; 2<br \/>\ny = -2x + 1<\/p>\n<p>Answer:<br \/>\nThe solution set is (1, -1).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\ny = x &#8211; 2 &#8212; (i)<br \/>\ny = -2x + 1 &#8212; (ii)<br \/>\nx &#8211; 2 = -2x + 1<br \/>\nx + 2x = 1 + 2<br \/>\n3x = 3<br \/>\nx = 1<br \/>\nSubstitute x = 1 in (i)<br \/>\ny = 1 &#8211; 2<br \/>\ny = -1<br \/>\nSo, the solution set is (1, -1).<\/p>\n<p>Question 15.<br \/>\n3y + 9 = 3x<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x + 1<\/p>\n<p>Answer:<br \/>\nThe solution set is (3, 0).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n3y + 9 = 3x &#8212; (i)<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x + 1 &#8212;- (ii)<br \/>\nSubstitute (ii) in (i)<br \/>\n3(-1\/3 x + 1) + 9 = 3x<br \/>\n-x + 3 + 9 = 3x<br \/>\n4x = 12<br \/>\nx = 3<br \/>\nSubstitute x = 3 in (i)<br \/>\n9 = 9 + 3y<br \/>\ny = 0<br \/>\nSo, the solution set is (3, 0).<\/p>\n<p>Question 16.<br \/>\n-x + 2y = -4<br \/>\n4y = x<\/p>\n<p>Answer:<br \/>\nThe solution set is (8, 2).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n-x + 2y = -4 &#8212;- (i)<br \/>\n4y = x &#8212;- (ii)<br \/>\nSubstitute (ii) in (i)<br \/>\n-4y + 2y = -4<br \/>\n-2y = -4<br \/>\ny = 2<br \/>\nSubstitute y = 2 in (ii)<br \/>\nx = 4(2)<br \/>\nx = 8<br \/>\nSo, the solution set is (8, 2).<\/p>\n<p>Question 17.<br \/>\nThe measure of an acute angle in a right triangle is one-fourth the measure of the other acute angle. Write a system of linear equations that represents this situation and use it to \ufb01nd the measures of the acute angles of the triangle.<\/p>\n<p>Answer:<br \/>\nx = 72 degrees, y = 18 degrees<\/p>\n<p>Explanation:<br \/>\nLet two acute angles be x, y<br \/>\nThe measure of an acute angle in a right triangle is one-fourth the measure of the other acute angle<br \/>\nx + y = 90 &#8212; (i)<br \/>\ny = 1\/4 x &#8212; (ii)<br \/>\nSubstitute (ii) in (i)<br \/>\nx + 1\/4 = 90<br \/>\n5\/4 x = 90<br \/>\nx = 90 . (4\/5)<br \/>\nx = 72 degrees<br \/>\nSo, y = 1\/4 (72)<br \/>\ny = 18 degrees<\/p>\n<p><strong>5.3 Solving Systems of Linear Equations by Elimination<\/strong> (pp. 211\u2013218)<\/p>\n<p><strong>Solve the system by elimination. Check your solution.<\/strong><\/p>\n<p>Question 18.<br \/>\n2x + 5y = 60<br \/>\n2x &#8211; 5y = -20<\/p>\n<p>Answer:<br \/>\nThe solution set is (10, 8).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n2x + 5y = 60 &#8212; (i)<br \/>\n2x &#8211; 5y = -20 &#8212; (ii)<br \/>\nAdd both equations<br \/>\n2x + 5y + 2x &#8211; 5y = 60 &#8211; 20<br \/>\n4x = 40<br \/>\nx = 10<br \/>\nSubstitute x = 10 in (i)<br \/>\n2(10) + 5y = 60<br \/>\n20 + 5y = 60<br \/>\n5y = 60 &#8211; 20<br \/>\n5y = 40<br \/>\ny = 8<br \/>\nSubstitute x = 10, y = 8 in (i)<br \/>\n2(10) + 5(8) = 20 + 40 = 60<br \/>\nSo, the solution set is (10, 8).<\/p>\n<p>Question 19.<br \/>\n4x &#8211; 3y = 15<br \/>\n2x + y = -5<\/p>\n<p>Answer:<br \/>\nThe solution set is (3\/2, -3).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n4x &#8211; 3y = 15 &#8212;- (i)<br \/>\n2x + y = -5 &#8212;- (ii)<br \/>\nMultiply (ii) by 3<br \/>\n6x + 3y = -15 &#8212;- (iii)<br \/>\nAdd (ii) &amp; (i)<br \/>\n4x &#8211; 3y + 6 + 3y = 15 &#8211; 15<br \/>\n4x &#8211; 6 = 0<br \/>\n4x = 6<br \/>\nx = 3\/2<br \/>\nSubstitute x = 3\/2 in (i)<br \/>\n4(3\/2) &#8211; 3y = 15<br \/>\n6 &#8211; 3y = 15<br \/>\n-3y = 15 &#8211; 6<br \/>\n-3y = 9<br \/>\ny = -3<br \/>\nSubstitute x = 3\/2, y = -3 in (i)<br \/>\n4(3\/2) &#8211; 3(-3) = 6 + 9 = 15<br \/>\nSo, the solution set is (3\/2, -3).<\/p>\n<p>Question 20.<br \/>\nA gift basket that contains jars of jam and packages of bread mix costs $45. There are 8 items in the basket. Jars of jam cost $6 each, and packages of bread mix cost $5 each. Write and solve a system of linear equations to \ufb01nd the number of each item in the gift basket.<\/p>\n<p>Answer:<br \/>\n5 jars of jam and 3 packages of bread mix.<\/p>\n<p>Explanation:<br \/>\nLet j be the no of jars of jam, b bethe no of packages of bread mix<br \/>\nj + b = 8<br \/>\n6j + 5b = 45<br \/>\n5j + 5b = 40<br \/>\n6j + 5b &#8211; 5j &#8211; 5b = 45 &#8211; 40<br \/>\nj = 5<br \/>\n5 + b = 8<br \/>\nb = 3<br \/>\nSo, 5 jars of jam and 3 packages of bread mix.<\/p>\n<p>Question 21.<br \/>\nWhen might it be easier to solve a system by elimination instead of graphing?<\/p>\n<p>Answer:<br \/>\nSubstitution is easier to solve a system by elimination instead of graphing.<\/p>\n<p>Question 22.<br \/>\nYou have a total of 10 coins consisting of nickels and dimes in your pocket. The value of the coins is $0.70. Write and solve a system of linear equations to \ufb01nd the numbers of nickels and dimes in your pocket.<\/p>\n<p>Answer:<br \/>\nThere are 6 nickels and 4 dimes.<\/p>\n<p>Explanation:<br \/>\nThe no of coins of nickles and dimes 10.<br \/>\nx + y = 10 &#8212; (i)<br \/>\n0.05x + 0.1y = 0.70 &#8212; (ii)<br \/>\nMultiply (i) by 0.05<br \/>\n0.05x + 0.05y = 0.5<br \/>\n0.05x + 0.1y &#8211; 0.05x &#8211; 0.05y = 0.70 &#8211; 0.50<br \/>\n0.05y = 0.2<br \/>\ny = 4<br \/>\nx + 4 = 10<br \/>\nx = 6<br \/>\nThere are 6 nickles and 4 dimes.<\/p>\n<p><strong>5.4 Solving Special Systems of Linear Equations<\/strong> (pp. 219\u2013224)<\/p>\n<p><strong>Solve the system. Explain your choice of method.<\/strong><\/p>\n<p>Question 23.<br \/>\nx + 2y = -5<br \/>\nx &#8211; 2y = -5<\/p>\n<p>Answer:<br \/>\nThe solution set is (-5, 0)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\nx + 2y = -5<br \/>\nx &#8211; 2y = -5<br \/>\nadd both equations<br \/>\nx + 2y + x &#8211; 2y = -5 &#8211; 5<br \/>\n2x = -10<br \/>\nx = -5<br \/>\nSubstitute x = -5 in x &#8211; 2y = -5<br \/>\n-5 &#8211; 2y = -5<br \/>\n-2y = 0<br \/>\ny = 0<br \/>\nSo, the solution set is (-5, 0)<\/p>\n<p>Question 24.<br \/>\n3x &#8211; 2y = 1<br \/>\n9x &#8211; 6y = 3<\/p>\n<p>Answer:<br \/>\nThe system has infinitely many solutions.<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n3x &#8211; 2y = 1 &#8212;- (i)<br \/>\n9x &#8211; 6y = 3 &#8212;- (ii)<br \/>\nMultiply (ii) by 1\/3<br \/>\n3x &#8211; 2y = 1 &#8212;- (iii)<br \/>\nBoth (iii) &amp; (ii) are samem so the system has infinitely many solutions.<\/p>\n<p>Question 25.<br \/>\n8x &#8211; 2y = 16<br \/>\n-4x + y = 8<\/p>\n<p>Answer:<br \/>\nThe system has no solution.<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n8x &#8211; 2y = 16 &#8212; (i)<br \/>\n-4x + y = 8 &#8212; (ii)<br \/>\nMultiply (i) by 1\/2<br \/>\n4x &#8211; y = 8 &#8212; (iii)<br \/>\nAdd (iii) &amp; (ii)<br \/>\n-4x + y &#8211; 4x + y = 8 + 8<br \/>\nSo, the system has no solution.<\/p>\n<p>Question 26.<br \/>\n4y = x &#8211; 8<br \/>\n&#8211;\\(\\frac{1}{4}\\)x + y = -1<\/p>\n<p>Answer:<br \/>\nThe system has no solution.<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n4y = x &#8211; 8<br \/>\n&#8211;\\(\\frac{1}{4}\\)x + y = -1<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-50279 size-medium\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-53-300x285.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 53\" width=\"300\" height=\"285\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-53-300x285.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-53.jpg 693w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nLines are parallel<br \/>\nSo, the system has no solution.<\/p>\n<p>Question 27.<br \/>\n-2x + y = -2<br \/>\n3x + y = 3<\/p>\n<p>Answer:<br \/>\nThe solution set is (1, 0).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n-2x + y = -2 &#8212;(i)<br \/>\n3x + y = 3 &#8212; (ii)<br \/>\nSubtract equations<br \/>\n-2x + y &#8211; 3x &#8211; y = -2 &#8211; 3<br \/>\n-5x = -5<br \/>\nx = 1<br \/>\nSubstitute x = 1 in (i)<br \/>\n-2(1) + y = -2<br \/>\n-2 + y = -2<br \/>\ny = 0<br \/>\nSubstitute x = 1, y = 0 in (i)<br \/>\n-2(1) + 0 = -2<br \/>\nSo, the solution set is (1, 0).<\/p>\n<p>Question 28.<br \/>\n3x = \\(\\frac{1}{3}\\)y + 2<br \/>\n9x &#8211; y =-6<\/p>\n<p>Answer:<br \/>\nThe system has no solution.<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n3x = \\(\\frac{1}{3}\\)y + 2<br \/>\n9x &#8211; y =-6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-54.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 54\" width=\"662\" height=\"647\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-54.jpg 662w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-54-300x293.jpg 300w\" sizes=\"(max-width: 662px) 100vw, 662px\" \/><br \/>\nThe lines are parallel<br \/>\nSo, the system has no solution.<\/p>\n<p>Question 29.<br \/>\nYou have $50 in your savings account and plan to deposit $10 each week. Your friend has $25 in her savings account and plans to also deposit $10 each week.<br \/>\na. Write a system of linear equations that represents this situation.<br \/>\nb. Will your friend\u2019s account ever have the same amount of money as your account? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32618\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-8-Chapter-5-Systems-of-Linear-Equations-102.png\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 102\" width=\"293\" height=\"226\" \/><\/p>\n<p>Answer:<br \/>\na. y = 10x + 50, y = 10x + 25<br \/>\nb. No, the amount will never be equal.<\/p>\n<p>Explanation:<br \/>\nLet the total amount be y and the number of weeks is x<br \/>\na. You have $50 in your savings account and plan to deposit $10 each week.<br \/>\ny = 10x + 50<br \/>\nYour friend has $25 in her savings account and plans to also deposit $10 each week.<br \/>\ny = 10x + 25<br \/>\nb. No, the account will never have the same amounts. By inspection, the lines are parallel and have the same slopes but different y-intercepts. So, the amount will always be $25 greater than the friend account but will not be the same.<\/p>\n<p><strong>Write a system of linear equations that \ufb01ts the description. Use a graph to justify your answer.<\/strong><\/p>\n<p>Question 30.<br \/>\nThe system has no solution.<\/p>\n<p>Answer:<br \/>\nThe possible systems of linear equations can be y = -5x &#8211; 2, 5x + y = 0.<\/p>\n<p>Explanation:<br \/>\nThe conditions where two equations have no solution are The lines should be parallel having the same slopes but different y-intercepts.<br \/>\nSo, let us consider the slope as -5 and different y-intercepts.<br \/>\nThen, the possible systems of linear equations can be y = -5x &#8211; 2, 5x + y = 0.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-50179 size-medium\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-38-300x296.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 38\" width=\"300\" height=\"296\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-38-300x296.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-38.jpg 663w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 31.<br \/>\nThe system has in\ufb01nitely many solutions.<\/p>\n<p>Answer:<br \/>\nThe system of linear equations can be 0.5x + 4y = -11, -1.5x &#8211; 12y = 33.<\/p>\n<p>Explanation:<br \/>\nThe condition is lines are the same and have the same slope, y-intercepts.<br \/>\nSo, the system of linear equations can be 0.5x + 4y = -11, -1.5x &#8211; 12y = 33<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50186\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-42.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 42\" width=\"657\" height=\"657\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-42.jpg 657w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-42-300x300.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-42-150x150.jpg 150w\" sizes=\"(max-width: 657px) 100vw, 657px\" \/><\/p>\n<p>Question 32.<br \/>\nThe system has one solution.<\/p>\n<p>Answer:<br \/>\nThe system of linear equations can be -2x + y = 1.3, 2(0.5x &#8211; y) = 4.6<\/p>\n<p>Explanation:<br \/>\nThe system has only one solution means the lines intersect and have different slopes.<br \/>\nSo, the system of linear equations can be -2x + y = 1.3, 2(0.5x &#8211; y) = 4.6<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-48.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 48\" width=\"539\" height=\"523\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-48.jpg 539w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-48-300x291.jpg 300w\" sizes=\"(max-width: 539px) 100vw, 539px\" \/><\/p>\n<p>Question 33.<br \/>\nSolve the system by graphing, by substitution, and by elimination. Which method do you prefer? Explain your reasoning.<br \/>\n5x + y = 8<br \/>\n2y = -10x + 8<\/p>\n<p>Answer:<br \/>\nThe system has no solution.<br \/>\nOut of all methods, I feel graphing is easier.<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n5x + y = 8 &#8212;- (i)<br \/>\n2y = -10x + 8 &#8212;- (ii)<br \/>\nGraph the above equations<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-50374 size-medium\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-55-300x300.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 55\" width=\"300\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-55-300x300.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-55-150x150.jpg 150w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-55.jpg 660w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe lines are parallel. So, the system has no solution.<br \/>\nUsing substitution method<br \/>\nMultiply equation (ii) by 1\/2<br \/>\n2y = -10x + 8<br \/>\ny = -5x + 4<br \/>\nSubstitute y = -5x + 4 in (i)<br \/>\n5x + -5x + 4 = 8<br \/>\n4 = 8<br \/>\nSo, the system has no solution<br \/>\nUsing elimination method<br \/>\ny = -5x + 4<br \/>\n5x + y = 4 &#8212; (iii)<br \/>\nSubtract (i) &amp; (iii)<br \/>\n5x + y &#8211; -5x &#8211; y = 8 &#8211; 4<br \/>\n0 = 4<br \/>\nSo, the system has no solution.<\/p>\n<p>Question 34.<br \/>\nYour friend chooses to solve the system of equations by graphing. Would you choose the same method? Why or why not?<br \/>\n5x + 2y = 12<br \/>\ny = x &#8211; 8<\/p>\n<p>Answer:<br \/>\nThe solution set is (4, -4).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n5x + 2y = 12, y = x &#8211; 8<br \/>\nYes, I will also choose graphing to solve the equations.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50376\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-56.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 56\" width=\"555\" height=\"539\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-56.jpg 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-56-300x291.jpg 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><br \/>\nThe solution set is (4, -4).<\/p>\n<h3><a id=\"Systems_of_Linear_Equations_Practice_Test\"><\/a>Systems of Linear Equations Practice Test<\/h3>\n<p><strong>5 Practice Test<\/strong><\/p>\n<p>Question 1.<br \/>\nSolve the system by graphing.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32619\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-103.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 103\" width=\"108\" height=\"77\" \/><\/p>\n<p>Answer:<br \/>\nThe solution is (4, 12).<\/p>\n<p>Explanation:<br \/>\nThe given systems of linear equations are y = 1\/2 x + 10, y = 4x &#8211; 4<br \/>\nGraph the equations<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-49550\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-23.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 23\" width=\"548\" height=\"539\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-23.jpg 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-23-300x295.jpg 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><br \/>\nThe lines intersect at (4, 12)<br \/>\nSo, the solution is (4, 12)<\/p>\n<p>Question 2.<br \/>\nSolve the system by substitution.<br \/>\n-3x + y = 2<br \/>\n-x + y &#8211; 4 = 0<\/p>\n<p>Answer:<br \/>\nThe solution set is (1, 5)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n-3x + y = 2<br \/>\ny = 2 + 3x &#8212;- (i)<br \/>\n-x + y &#8211; 4 = 0 &#8212;- (ii)<br \/>\nSubstitute (i) in (ii)<br \/>\n-x + 2 + 3x &#8211; 4 = 0<br \/>\n2x &#8211; 2 = 0<br \/>\n2x = 2<br \/>\nx = 1<br \/>\nSubstitute x = 1 in (i)<br \/>\ny = 2 + 3(1)<br \/>\ny = 2 + 3<br \/>\ny = 5<br \/>\nSo, the solution set is (1, 5)<\/p>\n<p>Question 3.<br \/>\nSolve the system by elimination. Solve the system. Check your solution.<br \/>\nx + y = 12<br \/>\n3x = 2y + 6<\/p>\n<p>Answer:<br \/>\nThe solution set is (-18, 30)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\nx + y = 12 &#8212;- (i)<br \/>\n3x = 2y + 6<br \/>\n3x &#8211; 2y = 6 &#8212;- (ii)<br \/>\nMultiply equation (i) by 2<br \/>\n2(x + y = 12)<br \/>\n2x + 2y = 24 &#8212;- (iii)<br \/>\nSubtract (ii) from (iii)<br \/>\n3x &#8211; 2y &#8211; 2x &#8211; 2y = 6 &#8211; 24<br \/>\nx = -18<br \/>\nSubstitute x = -18 in (i)<br \/>\n-18 + y = 12<br \/>\ny = 12 + 18<br \/>\ny = 30<br \/>\nSo, the solution set is (-18, 30)<\/p>\n<p>Question 4.<br \/>\nSolve the system. Explain your choice of method.<br \/>\n-2x + y + 3 = 0<br \/>\n3x + 4y = -1<\/p>\n<p>Answer:<br \/>\nThe solution set is (1, -1).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n-2x + y + 3 = 0<br \/>\n3x + 4y = -1<br \/>\nBy graphing<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50378\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-57.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 57\" width=\"535\" height=\"536\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-57.jpg 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-57-300x300.jpg 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-57-150x150.jpg 150w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><br \/>\nThe solution set is (1, -1).<\/p>\n<p><strong>Without graphing or solving, determine whether the system of linear equations has one solution, in\ufb01nitely many solutions, or no solution. Explain your reasoning.<\/strong><\/p>\n<p>Question 5.<br \/>\ny = 4x + 8<br \/>\ny = 5x + 1<\/p>\n<p>Answer:<br \/>\nThe system has one solution.<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\ny = 4x + 8 &#8212; (i)<br \/>\ny = 5x + 1 &#8212;- (ii)<br \/>\nEquate both equations<br \/>\n4x + 8 = 5x + 1<br \/>\n5x &#8211; 4x = 8 &#8211; 1<br \/>\nx = 7<br \/>\nSubstitute x = 7 in (i)<br \/>\ny = 4(7) + 8<br \/>\ny = 28 + 8<br \/>\ny = 36<br \/>\nSo, the system has one solution.<\/p>\n<p>Question 6.<br \/>\n2y = 16x &#8211; 2<br \/>\ny = 8x &#8211; 1<\/p>\n<p>Answer:<br \/>\nThe system has infinitely many solutions<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\n2y = 16x &#8211; 2 &#8212; (i)<br \/>\ny = 8x &#8211; 1 &#8212; (ii)<br \/>\nSubstitute (ii) in (i)<br \/>\n2(8x &#8211; 1) = 16x &#8211; 2<br \/>\n16x &#8211; 2 = 16x &#8211; 2<br \/>\nSo, the system has infinitely many solutions.<\/p>\n<p>Question 7.<br \/>\ny = -3x + 2<br \/>\n6x + 2y = 10<\/p>\n<p>Answer:<br \/>\nThe system has\u00a0 no solution.<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\ny = -3x + 2 &#8212; (i)<br \/>\n6x + 2y = 10 &#8212; (ii)<br \/>\nSubstitute (i) in (ii)<br \/>\n6x + 2(-3x + 2) = 10<br \/>\n6x &#8211; 6x + 4 = 10<br \/>\n4 = 10<br \/>\nSo, the system has\u00a0 no solution.<\/p>\n<p>Question 8.<br \/>\nIn the diagram, the measure of \u22201 is three times the measure of \u22202. Find the measure of each angle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32620\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-104.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 104\" width=\"205\" height=\"158\" \/><\/p>\n<p>Answer:<br \/>\n\u22201 = 3(\u22202) = \u22206<br \/>\n\u22203 = 180 &#8211; \u22202 = \u22205 = \u22207<br \/>\n\u22204 = \u22202<\/p>\n<p>Explanation:<br \/>\nThe measure of \u22201 is three times the measure of \u22202<br \/>\n\u22201 = 3(\u22202)<br \/>\n\u22205 + \u22202 = 180<br \/>\n\u22205 = 180 &#8211; \u22202<br \/>\n\u22206 + \u22201 = 180<br \/>\n\u22206 + 3(\u22202) = 180<br \/>\n\u22206 = 180 &#8211; 3(\u22202)<br \/>\n\u22202 + \u22203 = 180<br \/>\n\u22203 = 180 &#8211; \u22202 = \u22205<br \/>\nSo, \u22204 = \u22202<\/p>\n<p>Question 9.<br \/>\nThe price of 2 pears and 6 apples is $14. The price of 3 pears and 9 apples is $21. Can you determine the unit prices for pears and apples? Explain.<\/p>\n<p>Answer:<br \/>\nThey have infinitely many solutions.<\/p>\n<p>Explanation:<br \/>\nLet the price of 1 pears be x, price of 1 apple be y<br \/>\nThe price of 2 pears and 6 apples is $14<br \/>\n2x + 6y = 14 &#8212; (i)<br \/>\nx + 3y = 7<br \/>\nThe price of 3 pears and 9 apples is $21<br \/>\n3x + 9y = 21 &#8212;- (ii)<br \/>\nx + 3y = 7<br \/>\nBoth the equations are the same. So they have infinitely many solutions.<\/p>\n<p>Question 10.<br \/>\nA bouquet of lilies and tulips has 12 \ufb02owers. Lilies cost $3 each, and tulips cost $2 each. The bouquet costs $32. Write and solve a system of linear equations to \ufb01nd the numbers of lilies and tulips in the bouquet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32621\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-105.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 105\" width=\"244\" height=\"355\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-105.png 244w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-105-206x300.png 206w\" sizes=\"(max-width: 244px) 100vw, 244px\" \/><\/p>\n<p>Answer:<br \/>\n8 lilies and 4 tulips.<\/p>\n<p>Explanation:<br \/>\nLet l be the no of lilies, t be the no of tulips<br \/>\nA bouquet of lilies and tulips has 12 flowers<br \/>\nl + t = 12 &#8212;- (i)<br \/>\nLilies cost $3 each, and tulips cost $2 each. The bouquet costs $32.<br \/>\n3l + 2t = 32 &#8212; (ii)<br \/>\nMultiply (i) by 3<br \/>\n3(l + t = 12)<br \/>\n3l + 3t = 36 &#8212; (iii)<br \/>\nSubtract (iii) from (ii)<br \/>\n3l + 3t &#8211; (3l + 2t) = 36 &#8211; 32<br \/>\n3l + 3t &#8211; 3l &#8211; 2t = 4<br \/>\nt = 4<br \/>\nSubstitute t = 4 in (i)<br \/>\nl + 4 = 12<br \/>\nl = 12 &#8211; 4<br \/>\nl = 8<br \/>\n8 lilies and 4 tulips.<\/p>\n<p>Question 11.<br \/>\nHow much does it cost for 2 specials and 2 glasses of milk?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32622\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-106.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 106\" width=\"173\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-106.png 173w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-106-150x150.png 150w\" sizes=\"(max-width: 173px) 100vw, 173px\" \/><\/p>\n<p>Answer:<br \/>\nThe cost of 2 specials &amp; 2 glasses of milk is $16.1.<\/p>\n<p>Explanation:<br \/>\nLet specials be x and glasses of milk be y<br \/>\n4x + 2y = 28 &#8212; (i)<br \/>\n3x + 4y = 26.25 &#8212; (ii)<br \/>\n2(4x + 2y = 28)<br \/>\n8x + 4y = 56<br \/>\nsubtract equations<br \/>\n8x + 4y &#8211; (3x + 4y) = 56 &#8211; 26.25<br \/>\n8x + 4y &#8211; 3x &#8211; 4y = 29.75<br \/>\n5x = 29.75<br \/>\nx = 5.95<br \/>\nSubstitute x = 5.95 in (i)<br \/>\n4(5.95) + 2y = 28<br \/>\n23.8 + 2y = 28<br \/>\n2y = 28 &#8211; 23.8<br \/>\n2y = 4.2<br \/>\ny = 2.1<br \/>\nThe cost of 2 specials &amp; 2 glasses of milk is 2x + 2y<br \/>\n= 2(5.95) + 2(2.1)<br \/>\n= 11.9 + 4.2<br \/>\n= 16.1<br \/>\nThe cost of 2 specials &amp; 2 glasses of milk is $16.1.<\/p>\n<h3><a id=\"Systems_of_Linear_Equations_Cumulative_Practice\"><\/a>Systems of Linear Equations Cumulative Practice<\/h3>\n<p>Question 1.<br \/>\nWhat is the solution of the system of equations?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32623\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-107.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 107\" width=\"195\" height=\"132\" \/><br \/>\nB. (0, -1)<br \/>\nC. no solution<br \/>\nD. in\ufb01nitely many solutions<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-32624\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-108.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 108\" width=\"349\" height=\"383\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-108.png 349w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-108-273x300.png 273w\" sizes=\"(max-width: 349px) 100vw, 349px\" \/><\/p>\n<p>Answer:<br \/>\nB. (0, -1)<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\ny = 2\/3 x &#8211; 1<br \/>\n4x + 6y = -6<br \/>\nBy graphing<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50433\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-58.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 58\" width=\"530\" height=\"523\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-58.jpg 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-58-300x296.jpg 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><br \/>\nso, the solution set is (-1, 0)<\/p>\n<p>Question 2.<br \/>\nWhat is the value of x?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32625\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-109.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 109\" width=\"528\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-109.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-109-300x111.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Answer:<br \/>\nx = 40 degrees<\/p>\n<p>Explanation:<br \/>\nx + 140 = 180<br \/>\nx = 180 &#8211; 140<br \/>\nx = 40 degrees<\/p>\n<p>Question 3.<br \/>\nWhich of the following shows Rectangle E&#8217;F&#8217;G&#8217;H&#8217;, the image of Rectangle EFGH after it is translated 4 units down?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32626\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-110.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 110\" width=\"178\" height=\"124\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32627\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-111.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 111\" width=\"533\" height=\"318\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-111.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-111-300x179.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Answer:<br \/>\nF.<\/p>\n<p>Explanation:<br \/>\nBy observing all the images we can say that F is the answer.<\/p>\n<p>Question 4.<br \/>\nWhich point is a solution of the system of equations?<br \/>\nx + 3y = 10<br \/>\nx = 2y &#8211; 5<br \/>\nA. (1, 3)<br \/>\nB. (3, 1)<br \/>\nC. (55, -15)<br \/>\nD. (-35, -15)<\/p>\n<p>Answer:<br \/>\nThe solution set is (1, 3).<\/p>\n<p>Explanation:<br \/>\nThe given system of linear equations are<br \/>\nx + 3y = 10<br \/>\nx = 2y &#8211; 5<br \/>\nSubstitute x = 2y &#8211; 5 in x + 3y = 10<br \/>\n2y &#8211; 5\u00a0+ 3y = 10<br \/>\n5y = 10 + 5<br \/>\n5y = 15<br \/>\ny = 3<br \/>\nSubstitute y = 3 in x = 2y &#8211; 5<br \/>\nx = 2(3) &#8211; 5<br \/>\nx = 6 &#8211; 5<br \/>\nx = 1<br \/>\nSo, the solution set is (1, 3).<\/p>\n<p>Question 5.<br \/>\nThe graph of a system of two linear equations is shown. Which point is the solution of the system?<br \/>\nF. (-1, 2)<br \/>\nG. (0, 4)<br \/>\nH. (2, -1)<br \/>\nI. (0, 0)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32628\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-112.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 112\" width=\"201\" height=\"190\" \/><\/p>\n<p>Answer:<br \/>\nF. (-1, 2)<\/p>\n<p>Explanation:<br \/>\nFrom the graph, the point of intersection of two equations is (-1, 2)<br \/>\nSo, the solution set is (-1, 2).<\/p>\n<p>Question 6.<br \/>\nA scenic train ride has one price for adults and one price for children. One family of two adults and two children pays $62 for the train ride. Another family of one adult and four children pays $70. Which system of linear equations can you use to \ufb01nd the price x for an adult and the price y for a child?<br \/>\nA. 2x + 2y = 70<br \/>\nx + 4y = 62<br \/>\nB. x + y = 62<br \/>\nx + y = 70<br \/>\nC. 2x + 2y = 62<br \/>\n4x + y = 70<br \/>\nD. 2x + 2y = 62<br \/>\nx + 4y = 70<\/p>\n<p>Answer:<br \/>\nD. 2x + 2y = 62<br \/>\nx + 4y = 70<\/p>\n<p>Explanation:<br \/>\nIf x is the cost of an adult ticket, y is the cost of a child ticket, then<br \/>\nOne family of two adults and two children pays $62 for the train ride.<br \/>\n2x + 2y = 62<br \/>\nAnother family of one adult and four children pays $70.<br \/>\nx + 4y = 70.<\/p>\n<p>Question 7.<br \/>\nWhich of the following is true about the graph of the linear equation y =-7x + 5?<br \/>\nF. The slope is 5, and the y-intercept is -7.<br \/>\nG. The slope is -5, and the y-intercept is -7.<br \/>\nH. The slope is -7, and the y-intercept is -5.<br \/>\nI. The slope is -7, and the y-intercept is 5.<\/p>\n<p>Answer:<br \/>\nH. The slope is -7, and the y-intercept is -5.<\/p>\n<p>Explanation:<br \/>\nThe given equation is y =-7x + 5<br \/>\nThe equation in the form of y = mx + c<br \/>\nSo, slope m = -7, y-intercept c = 5<\/p>\n<p>Question 8.<br \/>\nWhat is the measure (in degrees) of the exterior angle of the triangle?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32629\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-113.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 113\" width=\"439\" height=\"103\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-113.png 439w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-113-300x70.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><\/p>\n<p>Answer:<br \/>\nThe exterior angle of the triangle is 127 degrees<\/p>\n<p>Explanation:<br \/>\nThe Sum of angles of a triangle is 180<br \/>\nx + 64 + y = 180<br \/>\nx + y = 180 &#8211; 64<br \/>\nx + y = 116<br \/>\ny = 116 &#8211; x &#8212; (i)<br \/>\nSum of unknown angle and exterior angle is 180<br \/>\ny + 2x + 1 = 180<br \/>\ny + 2x = 180 &#8211; 1<br \/>\n2x + y = 179 &#8212;(ii)<br \/>\nSubstitute (i) in (ii)<br \/>\n2x + 116 &#8211; x = 179<br \/>\nx + 116 = 179<br \/>\nx = 179 &#8211; 116<br \/>\nx = 63<br \/>\nSo, the exterior angle is (2x + 1) = 2(63) + 1<br \/>\n= 126 + 1 = 127 degrees<\/p>\n<p>Question 9.<br \/>\nThe graph of which equation is parallel to the line that passes through the points (-1, 5) and (4, 7)?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32630\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-114.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 114\" width=\"416\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-114.png 416w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-114-300x69.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><\/p>\n<p>Answer:<br \/>\nc.<\/p>\n<p>Explanation:<br \/>\nThe equation of a line pass through two points is (y &#8211; y\u2081) = [ =(y\u2082 &#8211; y\u2081)\/(x\u2082 &#8211; x\u2081)](x &#8211; x\u2081)<br \/>\nx\u2081 = -1, y\u2081 = 5, x\u2082 = 4, y\u2082 = 7<br \/>\nSo, (y &#8211; 5) = (7 &#8211; 5)\/(4 + 1)(x + 1)<br \/>\ny &#8211; 5 = 2\/5(x + 1)<br \/>\n5(y &#8211; 5) = 2(x + 1)<br \/>\n5y &#8211; 25 = 2x + 2<br \/>\n5y = 2x + 2 + 25<br \/>\n5y = 2x + 27<br \/>\ny = 2\/5 x + 27\/5<\/p>\n<p>Question 10.<br \/>\nYou buy 3 T-shirts and 2 pairs of shorts for $42.50. Your friend buys 5 T-shirts and 3 pairs of shorts for $67.50. Use a system of linear equations to \ufb01nd the cost of each T-shirt. Show your work and explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32631\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-115.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 115\" width=\"75\" height=\"67\" \/><\/p>\n<p>Answer:<br \/>\nThe cost of each T-shirt is $7.5.<\/p>\n<p>Explanation:<br \/>\nLet t be the price of a t-shirt, s be the price of a pair of shorts<br \/>\nYou buy 3 T-shirts and 2 pairs of shorts for $42.50.<br \/>\n3t + 2s = 42.50<br \/>\nYour friend buys 5 T-shirts and 3 pairs of shorts for $67.50<br \/>\n5t + 3s = 67.50<br \/>\nMultiply the first equation by 3 and second by 2 and then subtract two equations<br \/>\n3(3t + 2s = 42.50) \u279d 9t + 6s = 127.50<br \/>\n2(5t + 3s = 67.50) \u279d 10t + 6s = 135<br \/>\n10t + 6s &#8211; 9t &#8211; 6s = 135 &#8211; 127.50<br \/>\nt = 7.5<br \/>\nThe cost of each T-shirt is $7.5.<\/p>\n<p>Question 11.<br \/>\nThe red \ufb01gure is congruent to the blue \ufb01gure. Which of the following is a sequence of rigid motions between the \ufb01gures?<br \/>\nF.Translate the red triangle 6 units left and then 4 units down.<br \/>\nG. Re\ufb02ect the red triangle in the x-axis, and then translate 4 units down.<br \/>\nH. Re\ufb02ect the red triangle in the y-axis, and then translate 4 units down.<br \/>\nI. Rotate the red triangle 180\u00b0 clockwise about the origin.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-32632\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-8-Chapter-5-Systems-of-Linear-Equations-116.png\" alt=\"Big Ideas Math Solutions Grade 8 Chapter 5 Systems of Linear Equations 116\" width=\"195\" height=\"192\" \/><\/p>\n<p>Answer:<br \/>\nI. Rotate the red triangle 180\u00b0 clockwise about the origin.<\/p>\n<p>Explanation:<br \/>\nThe vertices of the red triangle is (1, 1), (4, 1), (3, 4)<br \/>\nThe vertices of the blue triangle are (-1, -3), (-4, -3), (-3, 0)<\/p>\n<p>Question 12.<br \/>\nWhich of the following is true about the graph of the linear equation y = 2?<br \/>\nA. The graph is a vertical line that passes through (2, 0).<br \/>\nB. The graph is a vertical line that passes through (0, 2).<br \/>\nC. The graph is a horizontal line that passes through (2, 0).<br \/>\nD. The graph is a horizontal line that passes through (0, 2).<\/p>\n<p>Answer:<br \/>\nC. The graph is a horizontal line that passes through (2, 0).<\/p>\n<p>Explanation:<br \/>\nThe graph for the linear equation y = 2 is<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-50442\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-59.jpg\" alt=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations 59\" width=\"660\" height=\"642\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-59.jpg 660w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/big-ideas-math-answers-grade-8-chapter-5-systems-of-linear-equations-59-300x292.jpg 300w\" sizes=\"(max-width: 660px) 100vw, 660px\" \/><\/p>\n<p>Question 13.<br \/>\nThe sum of one-third of a number and 10 is equal to 13. What is the number?<br \/>\nF. \\(\\frac{8}{3}\\)<br \/>\nG. 9<br \/>\nH. 29<br \/>\nI. 69<\/p>\n<p>Answer:<br \/>\nG. 9<\/p>\n<p>Explanation:<br \/>\nLet the number be n<br \/>\nThe sum of one-third of a number and 10 is equal to 13<br \/>\n1\/3 n + 10 = 13<br \/>\n1\/3 n = 13 &#8211; 10<br \/>\n1\/3 n = 3<br \/>\nn = 3 x 3<br \/>\nn = 9<\/p>\n<p>Question 14.<br \/>\nSolve the equation 4x + 7y = 16 for x.<br \/>\nA. x = 4 + \\(\\frac{7}{4}\\)y<br \/>\nB. x = 4 &#8211; \\(\\frac{7}{4}\\)y<br \/>\nC. x = 4 + \\(\\frac{4}{7}\\)y<br \/>\nD. x = 16 &#8211; 7y<\/p>\n<p>Answer:<br \/>\nB. x = 4 &#8211; \\(\\frac{7}{4}\\)y<\/p>\n<p>Explanation:<br \/>\nThe given equation is 4x + 7y = 16<br \/>\n4x = 16 &#8211; 7y<br \/>\nx = (16 &#8211; 7y)\/4<br \/>\nx = 4 &#8211; 7y\/4<\/p>\n<p><em>Conclusion:<\/em><\/p>\n<p>The solutions given in this Big Ideas Math Grade 8 Chapter 5 are prepared by the subject experts. So, don&#8217;t worry about the answers just go through the answers and try to solve the problems. Test your knowledge by practicing the questions in the practice test section. After solving them cross check the answers. Follow our ccssmathanswers.com to get the latest updates regarding all Grade 8 Chapters.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math Answers Grade 8 Chapter 5 include questions on System of Linear Equations by Graphing, Substitution, Elimination, Connecting Concepts, etc. All the Problems in the Big Ideas Grade 8 Ch 5 System of Linear Equations are provided in a simple and easy-to-understand language. Learn the problem-solving methods used by referring to our Big &#8230; <a title=\"Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-answers-grade-8-chapter-5\/\" aria-label=\"More on Big Ideas Math Answers Grade 8 Chapter 5 Systems of Linear Equations\">Read more<\/a><\/p>\n","protected":false},"author":12,"featured_media":89240,"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-Answers-Grade-8-Chapter-5.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/32517"}],"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\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=32517"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/32517\/revisions"}],"predecessor-version":[{"id":90362,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/32517\/revisions\/90362"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89240"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=32517"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=32517"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=32517"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}