{"id":6613,"date":"2022-03-28T20:24:03","date_gmt":"2022-03-28T14:54:03","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=6613"},"modified":"2022-04-07T12:46:59","modified_gmt":"2022-04-07T07:16:59","slug":"go-math-grade-8-answer-key-chapter-8-solving-systems-of-linear-equations","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-8-solving-systems-of-linear-equations\/","title":{"rendered":"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations"},"content":{"rendered":"<p>Students of Grade 8 can get a detailed explanation for all the questions in Go Math Answer Key Chapter 8 Solving Systems of Linear Equations. In addition to the exercise problems we also provide the solutions for the review test. So, go through all the answers and explanations provided by the math experts in Go Math Grade 8 Chapter 8 Solving Systems of Linear Equations Answer Key. Our aim is to provide easy and simple tricks to solve the problems in <a href=\"https:\/\/ccssmathanswers.com\/go-math-grade-8-answer-key\/\" target=\"_blank\" rel=\"noopener noreferrer\">Go Math Grade 8 Answer Key<\/a> Chapter 8 Solving Systems of Linear Equations.<\/p>\n<h2>Download Go Math Grade 8 Chapter 8 Solving Systems of Linear Equations Answer Key Pdf<\/h2>\n<p>Students who are interested to secure the highest marks in the exams are suggested to download the Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations pdf. All the solutions are provided in the pdf format as per the list of the chapters provided in the latest edition. Hence refer to Go Math 8th Grade Solution Key to learning the easy way of maths practice. Check the list of the topics covered in Chapter 8 Solving Systems of Linear Equations from the following section.<\/p>\n<p><strong>Lesson 1: Solving Systems of Linear Equations by Graphing<\/strong><\/p>\n<ul>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_by_Graphing_\u2013_Page_No._232\">Solving Systems of Linear Equations by Graphing \u2013 Page No. 232<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_by_Graphing_\u2013_Page_No._233\">Solving Systems of Linear Equations by Graphing \u2013 Page No. 233<\/a><\/li>\n<li><a href=\"#Solving_Systems_of_Linear_Equations_by_Graphing_Lesson_Check_\u2013_Page_No._234\">Solving Systems of Linear Equations by Graphing Lesson Check \u2013 Page No. 234<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 2: Solving Systems by Substitution<\/strong><\/p>\n<ul>\n<li><a href=\"#Solving_Systems_by_Substitution_\u2013_Page_No._240\">Solving Systems by Substitution \u2013 Page No. 240<\/a><\/li>\n<li><a href=\"#Solving_Systems_by_Substitution_\u2013_Page_No._241\">Solving Systems by Substitution \u2013 Page No. 241<\/a><\/li>\n<li><a href=\"#Solving_Systems_by_Substitution_Lesson_Check_\u2013_Page_No._242\">Solving Systems by Substitution Lesson Check \u2013 Page No. 242<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 3: Solving Systems by Elimination<\/strong><\/p>\n<ul>\n<li><a href=\"#Solving_Systems_by_Elimination_\u2013_Page_No._248\">Solving Systems by Elimination \u2013 Page No. 248<\/a><\/li>\n<li><a href=\"#Solving_Systems_by_Elimination_\u2013_Page_No._249\">Solving Systems by Elimination \u2013 Page No. 249<\/a><\/li>\n<li><a href=\"#Solving_Systems_by_Elimination_Lesson_Check_\u2013_Page_No._250\">Solving Systems by Elimination Lesson Check \u2013 Page No. 250<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 4: Solving Systems by Elimination with Multiplication<\/strong><\/p>\n<ul>\n<li><a href=\"#Solving_Systems_by_Elimination_with_Multiplication_\u2013_Page_No._256\">Solving Systems by Elimination with Multiplication \u2013 Page No. 256<\/a><\/li>\n<li><a href=\"#Solving_Systems_by_Elimination_with_Multiplication_\u2013_Page_No._257\">Solving Systems by Elimination with Multiplication \u2013 Page No. 257<\/a><\/li>\n<li><a href=\"#Solving_Systems_by_Elimination_with_Multiplication_Lesson_Check_\u2013_Page_No._258\">Solving Systems by Elimination with Multiplication Lesson Check \u2013 Page No. 258<\/a><\/li>\n<\/ul>\n<p><strong>Lesson 5: Solving Solving Special Systems<\/strong><\/p>\n<ul>\n<li><a href=\"#Solving_Solving_Special_Systems_\u2013_Page_No._262\">Solving Solving Special Systems \u2013 Page No. 262<\/a><\/li>\n<li><a href=\"#Solving_Solving_Special_Systems_\u2013_Page_No._263\">Solving Solving Special Systems \u2013 Page No. 263<\/a><\/li>\n<li><a href=\"#Solving_Solving_Special_Systems_Lesson_Check_\u2013_Page_No._264\">Solving Solving Special Systems Lesson Check \u2013 Page No. 264<\/a><\/li>\n<\/ul>\n<p><strong>Model Quiz<\/strong><\/p>\n<ul>\n<li><a href=\"#Model_Quiz_\u2013_Page_No._265\">Model Quiz \u2013 Page No. 265<\/a><\/li>\n<\/ul>\n<p><strong>Review<\/strong><\/p>\n<ul>\n<li><a href=\"#Mixed_Review_\u2013_Page_No._266\">Mixed Review \u2013 Page No. 266<\/a><\/li>\n<\/ul>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_by_Graphing_\u2013_Page_No._232\"><\/a>Guided Practice &#8211; Solving Systems of Linear Equations by Graphing &#8211; Page No. 232<\/h3>\n<p><strong>Solve each system by graphing.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\left\\{\\begin{array}{l}y=3 x-4 \\\\y=x+2\\end{array}\\right.\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6615 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-1.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson1: Solving Systems of Linear Equations by Graphing img 1\" width=\"264\" height=\"263\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-1.jpg 264w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-1-150x150.jpg 150w\" sizes=\"(max-width: 264px) 100vw, 264px\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-1-300x244.png\" alt=\"grade 8 chapter 8 image 1\" width=\"300\" height=\"244\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-1-300x244.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-1.png 693w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\ny = 3x &#8211; 4<br \/>\ny = x + 2<br \/>\nThe solution of thr linear system of equations is the intersection point of the two equations.<br \/>\n(3, 5) is the solution of the system of equations.<br \/>\nIf x = 3, y = 3(3) &#8211; 4 = 9 &#8211; 4 = 5; y = 3 + 2 = 5<br \/>\n5 = 5; True<\/p>\n<p>Question 2.<br \/>\n\\(\\left\\{\\begin{array}{l}x-3 y=2 \\\\-3x+9y=-6\\end{array}\\right.\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6616 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-2.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson1: Solving Systems of Linear Equations by Graphing img 2\" width=\"252\" height=\"261\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-2-300x161.png\" alt=\"grade 8 chapter 8 image 2\" width=\"300\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-2-300x161.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-2.png 703w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nInfinitely many solutions<\/p>\n<p>Explanation:<br \/>\nx &#8211; 3y = 2<br \/>\n-3x + 9y = -6<br \/>\nx &#8211; 3y &#8211; x = -x + 2<br \/>\n-3y = -x + 2<br \/>\ny = 1\/3 . x &#8211; 2\/3<br \/>\n-3x + 9y + 3x = 3x &#8211; 6<br \/>\n9y = 3x &#8211; 6<br \/>\ny = 3\/9 . x &#8211; 6\/9<br \/>\ny = 1\/3 . x &#8211; 2\/3<br \/>\nThe solution of the linear system of equations is the intersection of the two equations.<br \/>\nInfinitely many solutions<\/p>\n<p>Question 3.<br \/>\nMrs. Morales wrote a test with 15 questions covering spelling and vocabulary. Spelling questions (x) are worth 5 points and vocabulary questions (y) are worth 10 points. The maximum number of points possible on the test is 100.<br \/>\na. Write an equation in slope-intercept form to represent the number of questions on the test.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6617 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-3.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson1: Solving Systems of Linear Equations by Graphing img 3\" width=\"270\" height=\"262\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\ny = -x + 15<\/p>\n<p>Explanation:<br \/>\nMrs. Morales wrote a test with 15 questions covering spelling and vocabulary. Spelling questions (x) are worth 5 points and vocabulary questions (y) are worth 10 points.<br \/>\nx + y = 15<br \/>\nx + y &#8211; x = -x + 15<br \/>\ny = -x + 15<\/p>\n<p>Question 3.<br \/>\nb. Write an equation in slope-intercept form to represent the total number of points on the test.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\ny = -1\/2 . x + 10<\/p>\n<p>Explanation:<br \/>\nThe total number of points on test is 100<br \/>\n5x + 10y = 100<br \/>\n5x + 10y &#8211; 5x = -5x + 100<br \/>\n10y = -5x + 100<br \/>\ny = -5\/10 . x + 100\/10<br \/>\ny = -1\/2 . x + 10<\/p>\n<p>Question 3.<br \/>\nc. Graph the solutions of both equations.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-3-300x138.png\" alt=\"grade 8 chapter 8 image 3\" width=\"300\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-3-300x138.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-3-768x354.png 768w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-3.png 790w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Question 3.<br \/>\nd. Use your graph to tell how many of each question type are on the test.<br \/>\n_________ spelling questions<br \/>\n_________ vocabulary questions<\/p>\n<p>Answer:<br \/>\n10 spelling questions<br \/>\n5 vocabulary questions<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 4.<br \/>\nWhen you graph a system of linear equations, why does the intersection of the two lines represent the solution of the system?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nTo solve a system of linear equations means finding the solutions that satisfy all the equations of that system. When we graph a system of linear equations, the intersection point lies on the line of each equation, which means that satisfies all the equations. Therefore, it is considered to be the solution to that system.<\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_by_Graphing_\u2013_Page_No._233\"><\/a>Solving Systems of Linear Equations by Graphing &#8211; Page No. 233<\/h3>\n<p>Question 5.<br \/>\nVocabulary<br \/>\nA_________________ is a set of equations that have the same variables.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nsystem of equations<\/p>\n<p>Explanation:<br \/>\nA system of equations is a set of equations that have the same variables.<\/p>\n<p>Question 6.<br \/>\nEight friends started a business. They will wear either a baseball cap or a shirt imprinted with their logo while working. They want to spend exactly $36 on the shirts and caps. Shirts cost $6 each and caps cost $3 each.<br \/>\na. Write a system of equations to describe the situation. Let x represent the number of shirts and let y represent the number of caps.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n6x + 3y = 36<\/p>\n<p>Explanation:<br \/>\nThe sum of caps and shirts is 8. The total cost of caps and shirts is $36.<br \/>\nx + y = 8<br \/>\n6x + 3y = 36<\/p>\n<p>Question 6.<br \/>\nb. Graph the system. What is the solution and what does it represent?<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6618 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-4.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson1: Solving Systems of Linear Equations by Graphing img 4\" width=\"285\" height=\"289\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe solution is (4, 4)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-4-300x260.png\" alt=\"grade 8 chapter 8 image 4\" width=\"300\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-4-300x260.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-4.png 528w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\nx + y &#8211; x = -x + 8<br \/>\ny = -x + 8<br \/>\n6x + 3y &#8211; 6x = -6x + 36<br \/>\n3y = -6x + 36<br \/>\ny = -6\/2 . x + 36\/3<br \/>\ny = -2x + 12<br \/>\n(4, 4). They should order 4 shirts and 4 caps.<\/p>\n<p>Question 7.<br \/>\nMultistep The table shows the cost for bowling at two bowling alleys.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6619 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-5.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson1: Solving Systems of Linear Equations by Graphing img 5\" width=\"327\" height=\"138\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-5.jpg 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-5-300x127.jpg 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\na. Write a system of equations, with one equation describing the cost to bowl at Bowl-o-Rama and the other describing the cost to bowl at Bowling Pinz. For each equation, let x represent the number of games played and let y represent the total cost.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\ny = 2.5x + 2<br \/>\ny = 2x + 4<\/p>\n<p>Explanation:<br \/>\nCost at Bowl-o-Rama =&gt; y = 2.5x + 2<br \/>\nCost at Bowling Pinz =&gt; y = 2x + 4<\/p>\n<p>Question 7.<br \/>\nb. Graph the system. What is the solution and what does it represent?<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6620 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-6.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson1: Solving Systems of Linear Equations by Graphing img 6\" width=\"262\" height=\"280\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-5-280x300.png\" alt=\"grade 8 chapter 8 image 5\" width=\"280\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-5-280x300.png 280w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-5.png 436w\" sizes=\"(max-width: 280px) 100vw, 280px\" \/><\/p>\n<p>Explanation:<br \/>\nThe solution of the linear system of equations is the intersection of the two equations.<br \/>\n(4, 12)<br \/>\nWhen 4 games are played, the total cost is $12.<\/p>\n<h3><a id=\"Solving_Systems_of_Linear_Equations_by_Graphing_Lesson_Check_\u2013_Page_No._234\"><\/a>Solving Systems of Linear Equations by Graphing &#8211; Page No. 234<\/h3>\n<p>Question 8.<br \/>\nMulti-Step Jeremy runs 7 miles per week and increases his distance by 1 mile each week. Tony runs 3 miles per week and increases his distance by 2 miles each week. In how many weeks will Jeremy and Tony be running the same distance? What will that distance be?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nAfter 4 weeks Jeremy and Tony will be running the same distance and that distance would be 11 miles.<\/p>\n<p>Explanation:<br \/>\nMulti-Step Jeremy runs 7 miles per week and increases his distance by 1 mile each week.<br \/>\ny = x + 7<br \/>\nTony runs 3 miles per week and increases his distance by 2 miles each week.<br \/>\ny = 2x + 3<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-6-300x229.png\" alt=\"grade 8 chapter 8 image 6\" width=\"300\" height=\"229\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-6-300x229.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-6.png 450w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe solution of the system of linear equation is (4, 11) which means that after 4 weeks Jeremy and Tony will be running the same distance and that distance would be 11 miles.<\/p>\n<p>Question 9.<br \/>\nCritical Thinking Write a real-world situation that could be represented by the system of equations shown below.<br \/>\n\\(\\left\\{\\begin{array}{l}y=4 x+10 \\\\y=3x+15\\end{array}\\right.\\)<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe entry fee of the first gym is $10 and for every hour that you spend there, you pay an extra $4. If we denote with x the number of hours that somebody spends at the gym and with y the total cost is<br \/>\ny = 4x + 10<br \/>\nThe entry fee of the second gym is $15 and for every hour that you spend there, you pay an extra $3. If we denote with x the number of hours that somebody spends at the gym and with y the total cost is<br \/>\ny = 3x + 15<br \/>\ny = 4x + 10<br \/>\ny = 3x + 15<\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 10.<br \/>\nMultistep The table shows two options provided by a high-speed Internet provider.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6621 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-7.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson1: Solving Systems of Linear Equations by Graphing img 7\" width=\"422\" height=\"133\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-7.jpg 422w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-7-300x95.jpg 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><br \/>\na. In how many months will the total cost of both options be the same? What will that cost be?<br \/>\n________ months<br \/>\n$ ________<\/p>\n<p>Answer:<br \/>\n5 months<br \/>\n$ 200<\/p>\n<p>Explanation:<br \/>\nLet y be the total cost after x month<br \/>\ny = 30x + 50<br \/>\nLet y be the total cost after x month<br \/>\ny = 40x<br \/>\nSubstitute y = 40x in y = 30x + 50<br \/>\n40x = 30x + 50<br \/>\n40x &#8211; 30x = 50<br \/>\n10x = 50<br \/>\nx = 50\/10<br \/>\nx = 5<br \/>\nThe total cost of both options will be the same after 5 months. Total cost would be y = 40(5) = $200.<\/p>\n<p>Question 10.<br \/>\nb. If you plan to cancel your Internet service after 9 months, which is the cheaper option? Explain.<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nWhen x = 9 months<br \/>\ny = 30(9) + 50 = $320<br \/>\ny = 40(9) = $360<br \/>\n$320 &lt; $360<br \/>\nOption 1 is cheaper as the total cost is less for option 1<\/p>\n<p>Question 11.<br \/>\nDraw Conclusions How many solutions does the system formed by x \u2212 y = 3 and ay \u2212 ax + 3a = 0 have for a nonzero number a? Explain.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nx &#8211; y = 3<br \/>\nay &#8211; ax + 3a =0<br \/>\nay &#8211; ax + 3a &#8211; 3a = 0 &#8211; 3a<br \/>\nay &#8211; ax = &#8211; 3a<br \/>\na(y &#8211; x) = -3a<br \/>\ny &#8211; x = -3<br \/>\nx &#8211; y = 3<br \/>\nBoth equations are the same. The system of linear equations have infinitely many solutions.<\/p>\n<h3><a id=\"Solving_Systems_by_Substitution_\u2013_Page_No._240\"><\/a>Guided Practice &#8211; Solving Systems by Substitution &#8211; Page No. 240<\/h3>\n<p><strong>Solve each system of linear equations by substitution.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\left\\{\\begin{array}{l}3x-2y=9 \\\\y=2x-7\\end{array}\\right.\\)<br \/>\nx = ________<br \/>\ny = ________<\/p>\n<p>Answer:<br \/>\nx = 5<br \/>\ny = 3<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}3x-2y=9 \\\\y=2x-7\\end{array}\\right.\\)<br \/>\nSubstitute 2x &#8211; 7 in 3x &#8211; 2y = 9<br \/>\n3x &#8211; 2(2x &#8211; 7) = 9<br \/>\n3x &#8211; 4x + 14 = 9<br \/>\n-x + 14 = 9<br \/>\n-x + 14 &#8211; 14 = 9 &#8211; 14<br \/>\n-x = -5<br \/>\nx = -5\/-1 = 5<br \/>\ny = 2(5) &#8211; 7 = 3<br \/>\nSolution is (5, 3)<\/p>\n<p>Question 2.<br \/>\n\\(\\left\\{\\begin{array}{l}y=x-4 \\\\2x+y=5\\end{array}\\right.\\)<br \/>\nx = ________<br \/>\ny = ________<\/p>\n<p>Answer:<br \/>\nx = 3<br \/>\ny = -1<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}y=x-4 \\\\2x+y=5\\end{array}\\right.\\)<br \/>\n2x + x &#8211; 4 = 5<br \/>\n3x &#8211; 4 = 5<br \/>\n3x &#8211; 4 + 4 = 5 + 4<br \/>\n3x = 9<br \/>\nx = 9\/3 = 3<br \/>\ny = 3 &#8211; 4 = -1<br \/>\nThe solution is (3, -1)<\/p>\n<p>Question 3.<br \/>\n\\(\\left\\{\\begin{array}{l}x+4y=6 \\\\y=-x+3\\end{array}\\right.\\)<br \/>\nx = ________<br \/>\ny = ________<\/p>\n<p>Answer:<br \/>\nx = 2<br \/>\ny = 1<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}x+4y=6 \\\\y=-x+3\\end{array}\\right.\\)<br \/>\nSubstitute y = -x + 3 in x + 4y = 6<br \/>\nx + 4(-x + 3) = 6<br \/>\nx &#8211; 4x + 12 = 6<br \/>\n-3x + 12 = 6<br \/>\n-3x + 12 &#8211; 12 = 6 &#8211; 12<br \/>\n-3x = -6<br \/>\nx = -6\/-3 = 2<br \/>\ny = -2 + 3 = 1<br \/>\nThe solution is (2, 1)<\/p>\n<p>Question 4.<br \/>\n\\(\\left\\{\\begin{array}{l}x+2y=6 \\\\x-y=3\\end{array}\\right.\\)<br \/>\nx = ________<br \/>\ny = ________<\/p>\n<p>Answer:<br \/>\nx = 4<br \/>\ny = 1<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}x+2y=6 \\\\x-y=3\\end{array}\\right.\\)<br \/>\ny = x &#8211; 3<br \/>\nSubstitute y = x &#8211; 3 in x + 2y = 6<br \/>\nx + 2(x &#8211; 3) = 6<br \/>\nx + 2x &#8211; 6 = 6<br \/>\n3x = 12<br \/>\nx = 12\/3<br \/>\nx = 4<br \/>\n4 &#8211; y = 3<br \/>\n-y = 3 &#8211; 4<br \/>\n-y = -1<br \/>\ny = 1<br \/>\nThe solution is (4, 1)<\/p>\n<p><strong>Solve each system. Estimate the solution first.<\/strong><\/p>\n<p>Question 5.<br \/>\n\\(\\left\\{\\begin{array}{l}6x+y=4 \\\\x-4y=19\\end{array}\\right.\\)<br \/>\nEstimate ______________<br \/>\nSolution ______________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nEstimate (2, -5)<br \/>\nSolution (1.4, -4.4)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}6x+y=4 \\\\x-4y=19\\end{array}\\right.\\)<br \/>\nLet&#8217;s find the estimation by graphing the equations<br \/>\nEstimate: (2, -5)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-7-300x260.png\" alt=\"grade 8 chapter 8 image 7\" width=\"300\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-7-300x260.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-7.png 579w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nx = 4y + 19<br \/>\n6(4y + 19) + y = 4<br \/>\n24y + 114 + y = 4<br \/>\n25y + 114 = 4<br \/>\n25y = 4 &#8211; 114<br \/>\n25y = -110<br \/>\ny = -110\/25<br \/>\ny = -4.4<br \/>\nx + 4(-4.4) = 19<br \/>\nx + 17.6 = 19<br \/>\nx = 19 &#8211; 17.6<br \/>\nx = 1.4<br \/>\nThe solution is (1.4, -4.4)<\/p>\n<p>Question 6.<br \/>\n\\(\\left\\{\\begin{array}{l}x+2y=8 \\\\3x+2y=6\\end{array}\\right.\\)<br \/>\nEstimate ______________<br \/>\nSolution ______________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nEstimate (-1, 5)<br \/>\nSolution (-1, 4.5)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}x+2y=8 \\\\3x+2y=6\\end{array}\\right.\\)<br \/>\nLet&#8217;s find the estimation by graphing the equations<br \/>\nEstimate: (-1, 5)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-8-300x208.png\" alt=\"grade 8 chapter 8 image 8\" width=\"300\" height=\"208\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-8-300x208.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-8.png 645w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nx = -2y + 8<br \/>\nSubstitute the equation x = -2y + 8 in 3x + 2y = 6<br \/>\n3(-2y + 8) + 2y = 6<br \/>\n-6y + 24 + 2y = 6<br \/>\n-4y = 6 &#8211; 24<br \/>\n-4y = -18<br \/>\ny = -18\/-4<br \/>\ny = 4.5<br \/>\nx + 2(4.5) = 8<br \/>\nx + 9 = 8<br \/>\nx = 8 &#8211; 9<br \/>\nx = -1<br \/>\nThe solution is (-1, 4.5)<\/p>\n<p>Question 7.<br \/>\n\\(\\left\\{\\begin{array}{l}3x+y=4 \\\\5x-y=22\\end{array}\\right.\\)<br \/>\nEstimate ______________<br \/>\nSolution ______________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nEstimate (3, -6)<br \/>\nSolution (3.25, -5.75)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}3x+y=4 \\\\5x-y=22\\end{array}\\right.\\)<br \/>\nFind the Estimation using graphing the equations.<br \/>\nEstimate: (3, -6)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-9-300x291.png\" alt=\"grade 8 chapter 8 image 9\" width=\"300\" height=\"291\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-9-300x291.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-9.png 513w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\ny = -3x + 4<br \/>\nSubstitute y = -3x + 4 in 5x &#8211; y = 22<br \/>\n5x &#8211; (-3x + 4) = 22<br \/>\n5x + 3x -4 = 22<br \/>\n8x = 26<br \/>\nx = 26\/8<br \/>\nx = 3.25<br \/>\n3(3.25) + y = 4<br \/>\n9.75 + y = 4<br \/>\ny = 4 &#8211; 9.75<br \/>\ny = -5.75<br \/>\nThe solution is (3.25, -5.75)<\/p>\n<p>Question 8.<br \/>\n\\(\\left\\{\\begin{array}{l}2x+7y=2 \\\\x+y=-1\\end{array}\\right.\\)<br \/>\nEstimate ______________<br \/>\nSolution ______________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nEstimate (-2, 1)<br \/>\nSolution (-1.8, 0.8)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}2x+7y=2 \\\\x+y=-1\\end{array}\\right.\\)<br \/>\nFind the Estimation using graphing the equations.<br \/>\nEstimate: (-2, 1)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-10-300x267.png\" alt=\"grade 8 chapter 8 image 10\" width=\"300\" height=\"267\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-10-300x267.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-10.png 616w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\ny = -x -1<br \/>\nSubstitute y = -x &#8211; 1 in 2x + 7y = 2<br \/>\n2x + 7(-x &#8211; 1) = 2<br \/>\n2x &#8211; 7x -7 = 2<br \/>\n-5x = 2 + 7<br \/>\n-5x = 9<br \/>\nx = -9\/5<br \/>\nx = -1.8<br \/>\n-1.8 + y = -1<br \/>\ny = -1 + 1.8<br \/>\ny = 0.8<br \/>\nThe solution is (-1.8, 0.8)<\/p>\n<p>Question 9.<br \/>\nAdult tickets to Space City amusement park cost x dollars. Children\u2019s tickets cost y dollars. The Henson family bought 3 adult and 1 child tickets for $163. The Garcia family bought 2 adult and 3 child tickets for $174.<br \/>\na. Write equations to represent the Hensons\u2019 cost and the Garcias\u2019 cost.<br \/>\nHensons\u2019 cost: ________________<br \/>\nGarcias\u2019 cost:__________________<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nHensons\u2019 cost: 3x + y = 163<br \/>\nGarcias\u2019 cost: 2x + 3y = 174<\/p>\n<p>Explanation:<br \/>\nHenson&#8217;s cost<br \/>\n3x + y = 163<br \/>\nGarcia&#8217;s cost<br \/>\n2x + 3y = 174<\/p>\n<p>Question 9.<br \/>\nb. Solve the system.<br \/>\nadult ticket price: $ _________<br \/>\nGarcias\u2019 cost: $ _________<\/p>\n<p>Answer:<br \/>\nadult ticket price: $ 45<br \/>\nGarcias\u2019 cost: $ 28<\/p>\n<p>Explanation:<br \/>\ny = -3x + 163<br \/>\nSubstitute y = -3x + 163 in 2x + 3y = 174<br \/>\n2x + 3(-3x + 163) = 174<br \/>\n2x -9x + 489 = 174<br \/>\n-7x = -315<br \/>\nx = -315\/-7 = 45<br \/>\n3(45) + y = 163<br \/>\n135 + y = 163<br \/>\ny = 163 &#8211; 135<br \/>\ny = 28<br \/>\nadult ticket price: $ 45<br \/>\nGarcias\u2019 cost: $ 28<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 10.<br \/>\nHow can you decide which variable to solve for first when you are solving a linear system by substitution?<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe variable with the unit coefficient should be solved first when solving a linear system by substitution.<\/p>\n<h3><a id=\"Solving_Systems_by_Substitution_\u2013_Page_No._241\"><\/a>8.2 Independent Practice &#8211; Solving Systems by Substitution &#8211; Page No. 241<\/h3>\n<p>Question 11.<br \/>\nCheck for Reasonableness Zach solves the system<br \/>\n\\(\\left\\{\\begin{array}{l}x+y=-3 \\\\x-y=1\\end{array}\\right.\\)<br \/>\nand finds the solution (1, -2). Use a graph to explain whether Zach\u2019s solution is reasonable.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6622 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-8.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 2: Solving Systems by Substitution img 8\" width=\"223\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-8.jpg 223w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-8-150x150.jpg 150w\" sizes=\"(max-width: 223px) 100vw, 223px\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-11-300x250.png\" alt=\"grade 8 chapter 8 image 11\" width=\"300\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-11-300x250.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-11.png 662w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}x+y=-3 \\\\x-y=1\\end{array}\\right.\\)<br \/>\nThe x coordinate of the solution is negative, hence Zach&#8217;s solution is not reasonable.<\/p>\n<p>Represent Real-World Problems Angelo bought apples and bananas at the fruit stand. He bought 20 pieces of fruit and spent $11.50. Apples cost $0.50 and bananas cost $0.75 each.<br \/>\na. Write a system of equations to model the problem. (Hint: One equation will represent the number of pieces of fruit. A second equation will represent the money spent on the fruit.)<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6623 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-9.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 2: Solving Systems by Substitution img 9\" width=\"215\" height=\"214\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-9.jpg 215w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-9-150x150.jpg 150w\" sizes=\"(max-width: 215px) 100vw, 215px\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nx + y = 20<br \/>\n0.5x + 0.75y = 11.5<\/p>\n<p>Explanation:<br \/>\nx + y = 20<br \/>\n0.5x + 0.75y = 11.5<br \/>\nwhere c is the number of Apples and y is the number of Bananas.<\/p>\n<p>Question 12.<br \/>\nb. Solve the system algebraically. Tell how many apples and bananas Angelo bought.<br \/>\n________ apples<br \/>\n________ bananas<\/p>\n<p>Answer:<br \/>\n14 apples<br \/>\n6 bananas<\/p>\n<p>Explanation:<br \/>\ny = -x + 20<br \/>\nSubstitute y = -x + 20 in 0.5x + 0.75y = 11.5<br \/>\n0.5x + 0.75(-x + 20) = 11.5<br \/>\n0.5x &#8211; 0.75x + 15 = 11.5<br \/>\n-0.25x + 15 = 11.5<br \/>\n-0.25x = 11.5 &#8211; 15<br \/>\n-0.25x = -3.5<br \/>\nx = -3.5\/-0.25<br \/>\nx = 14<br \/>\n14 + y = 20<br \/>\ny = 6<br \/>\nAngelo bought 14 apples and 6 bananas.<\/p>\n<p>Question 13.<br \/>\nRepresent Real-World Problems A jar contains n nickels and d dimes. There is a total of 200 coins in the jar. The value of the coins is $14.00. How many nickels and how many dimes are in the jar?<br \/>\n________ nickels<br \/>\n________ dimes<\/p>\n<p>Answer:<br \/>\n120 nickels<br \/>\n80 dimes<\/p>\n<p>Explanation:<br \/>\nA jar contains n nickels and d dimes. There is a total of 200 coins in the jar. The value of the coins is $14.00.<br \/>\n$14 = 1400 cents<br \/>\nn + d = 200<br \/>\n5n + 10d = 1400<br \/>\nd = -n + 200<br \/>\n5n + 10(-n + 200) = 1400<br \/>\n5n &#8211; 10n + 2000 = 1400<br \/>\n-5n = -600<br \/>\nn = -600\/-5<br \/>\nn = 120<br \/>\n120 + d = 200<br \/>\nd = 200 &#8211; 120<br \/>\nd = 80<br \/>\nThere are 120 nickles and 80 dimes in the jar.<\/p>\n<p>Question 14.<br \/>\nMultistep The graph shows a triangle formed by the x-axis, the line 3x\u22122y=0, and the line x+2y=10. Follow these steps to find the area of the triangle.<br \/>\na. Find the coordinates of point A by solving the system<br \/>\n\\(\\left\\{\\begin{array}{l}3x-2y=0 \\\\x-2y=10\\end{array}\\right.\\)<br \/>\nPoint A: ____________________<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6624 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-10.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 2: Solving Systems by Substitution img 10\" width=\"187\" height=\"190\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nPoint A: (2.5, 3.75)Coordinate of A is (2.5, 3.75)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}3x-2y=0 \\\\x-2y=10\\end{array}\\right.\\)<br \/>\nx = -2y + 10<br \/>\nSubstitute x = -2y + 10 in 3x &#8211; 2y = 0<br \/>\n3(-2y + 10) -2y = 0<br \/>\n-6y + 30 &#8211; 2y = 0<br \/>\n-8y = -30<br \/>\ny = -30\/-8 = 3.75<br \/>\nx + 2(3.75) = 10<br \/>\nx + 7.5 = 10<br \/>\nx = 10 &#8211; 7.5<br \/>\nx = 2.5<br \/>\nCoordinate of A is (2.5, 3.75)<\/p>\n<p>Question 14.<br \/>\nb. Use the coordinates of point A to find the height of the triangle.<br \/>\nheight:__________________<br \/>\nheight: \\(\\frac{\u25a1}{\u25a1}\\) units<\/p>\n<p>Answer:<br \/>\nheight: 3.75<br \/>\nheight: \\(\\frac{15}{4}\\) units<\/p>\n<p>Explanation:<br \/>\nHeight of the triangle is the y coordinate of A<br \/>\nHeight = 3.75<\/p>\n<p>Question 14.<br \/>\nc. What is the length of the base of the triangle?<br \/>\nbase:________________<br \/>\nbase: ______ units<\/p>\n<p>Answer:<br \/>\nbase: 10 units<\/p>\n<p>Explanation:<br \/>\nLength of the base = 10<\/p>\n<p>Question 14.<br \/>\nd. What is the area of the triangle?<br \/>\nA = ______ \\(\\frac{\u25a1}{\u25a1}\\) square units<\/p>\n<p>Answer:<br \/>\nA = 18.75 square units<br \/>\nA = 18 \\(\\frac{3}{4}\\) square units<\/p>\n<p>Explanation:<br \/>\nArea of the triangle = 1\/2 . Height . Base<br \/>\nArea = 1\/2 . 3.75 . 10 = 18.75<\/p>\n<h3><a id=\"Solving_Systems_by_Substitution_Lesson_Check_\u2013_Page_No._242\"><\/a>Solving Systems by Substitution &#8211; Page No. 242<\/h3>\n<p>Question 15.<br \/>\nJed is graphing the design for a kite on a coordinate grid. The four vertices of the kite are at A(\u2212\\(\\frac{4}{3}\\), \\(\\frac{2}{3}\\)), B(\\(\\frac{14}{3}\\), \u2212\\(\\frac{4}{3}\\)), C(\\(\\frac{14}{3}\\), \u2212\\(\\frac{16}{3}\\)), and D(\\(\\frac{2}{3}\\), \u2212\\(\\frac{16}{3}\\)). One kite strut will connect points A and C. The other will connect points B and D. Find the point where the struts cross.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6625 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-11.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 2: Solving Systems by Substitution img 11\" width=\"229\" height=\"305\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-11.jpg 229w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-11-225x300.jpg 225w\" sizes=\"(max-width: 229px) 100vw, 229px\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe struts cross as (8\/3, 10\/3)<\/p>\n<p>Explanation:<br \/>\n1. From AC<br \/>\nSlope = (y2 &#8211; y1)\/(x2 &#8211; x1) = [(-16\/3)-(2\/3)] \u00f7 [(14\/3) &#8211; (-4\/3)] = (-18\/3) \u00f7 (18\/3) = -1<br \/>\ny = mx + b<br \/>\n2\/3 = -1(-4\/3) + b<br \/>\n2\/3 = 4\/3 + b<br \/>\n1. From BD<br \/>\nSlope = (y2 &#8211; y1)\/(x2 &#8211; x1) = [(-16\/3)-(-4\/3)] \u00f7 [(2\/3) &#8211; (144\/3)] = (-12\/3) \u00f7 (-12\/3) = 1<br \/>\ny = mx + b<br \/>\n-4\/3 = 1(14\/3) + b<br \/>\n-4\/3 = 14\/3 + b<br \/>\n-18\/3 = b<br \/>\n-6 = b<br \/>\ny = mx + b<br \/>\ny = x -6<br \/>\n3. y = -x -2\/3<br \/>\ny = x &#8211; 6<br \/>\n4. y = -x &#8211; 2\/3<br \/>\nx &#8211; 6 = -x &#8211; 2\/3<br \/>\nx = -x &#8211; 2\/3 + 6<br \/>\nx = &#8211; x + 16\/3<br \/>\n2x = 16\/3<br \/>\nx = 16\/6<br \/>\nx = 8\/3<br \/>\nthen y = x &#8211; 6<br \/>\ny = 8\/3 &#8211; 18\/3<br \/>\ny = -10\/3<br \/>\nThe struts cross as (8\/3, 10\/3)<\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 16.<br \/>\nAnalyze Relationships Consider the system<br \/>\n\\(\\left\\{\\begin{array}{l}6x-3y=15 \\\\x+3y=-8\\end{array}\\right.\\)<br \/>\nDescribe three different substitution methods that can be used to solve this system. Then solve the system.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n(1, -3) is the answer.<\/p>\n<p>Explanation:<br \/>\nAs there are three different substitution methods, we can write<br \/>\nSolve for y in the first equation, then substitute that value into the second equation.<br \/>\nSolve for x in the second equation, then substitute that value into the first equation.<br \/>\nSolve either equation for 3y, then substitute that value into the other equation.<br \/>\nFrom the Second method,<br \/>\nx + 3y = -8<br \/>\nx = -3y &#8211; 8<br \/>\n6x &#8211; 3y = 15<br \/>\n6 (-3y &#8211; 8) -3y = 15<br \/>\n-18y &#8211; 48 -3y = 15<br \/>\n-21y &#8211; 48 = 15<br \/>\n-21y = 63<br \/>\ny = -3<br \/>\nx + 3y = -8<br \/>\nx + 3(-3) = -8<br \/>\nx &#8211; 9 = -8<br \/>\nx = 1<br \/>\n(1, -3) is the answer.<\/p>\n<p>Question 17.<br \/>\nCommunicate Mathematical Ideas Explain the advantages, if any, that solving a system of linear equations by substitution has over solving the same system by graphing.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe advantage of solving a system of linear equations by graphing is that it is relatively easy to do and requires very little algebra.<\/p>\n<p>Question 18.<br \/>\nPersevere in Problem Solving Create a system of equations of the form<br \/>\n\\(\\left\\{\\begin{array}{l}Ax+By=C \\\\Dx+Ey=F\\end{array}\\right.\\)<br \/>\nthat has (7, \u22122) as its solution. Explain how you found the system.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nx + y = 5<br \/>\nx &#8211; y = 9<br \/>\nsolves in :<br \/>\nx = (5+9)\/2 = 7<br \/>\ny = 5-9)\/2 = -2<br \/>\nA=1, B=2, C= 5<br \/>\nD=1, E= -1, F=9<br \/>\nx = 7<br \/>\ny = -2<br \/>\nIS a system (even if it is a trivial one) of equations so this answer would be acceptable.<br \/>\nThe target for a system is to find it SOLUTION SET and not to conclude with x=a and y=b<\/p>\n<h3><a id=\"Solving_Systems_by_Elimination_\u2013_Page_No._248\"><\/a>Guided Practice &#8211; Solving Systems by Elimination &#8211; Page No. 248<\/h3>\n<p>Question 1.<br \/>\nSolve the system<br \/>\n\\(\\left\\{\\begin{array}{l}4x+3y=1 \\\\x-3y=-11\\end{array}\\right.\\)<br \/>\nby adding.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6626 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-12.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 3: Solving Systems by Elimination img 12\" width=\"692\" height=\"307\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-12.jpg 692w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-12-300x133.jpg 300w\" sizes=\"(max-width: 692px) 100vw, 692px\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n4x + 3y = 1<br \/>\nx &#8211; 3y = -11<br \/>\nAdd the above two equations<br \/>\n4x + 3y = 1<br \/>\n+(x &#8211; 3y = -11)<br \/>\nAdd to eliminate the variable y<br \/>\n5x + 0y = -10<br \/>\nSimplify and solve for x<br \/>\n5x = -10<br \/>\nDivide both sided by 5<br \/>\nx = -10\/5 = -2<br \/>\nSubstitute into one of the original equations and solve for y.<br \/>\n4(-2) + 3y = 1<br \/>\n-8 + 3y = 1<br \/>\n3y = 9<br \/>\ny = 9\/3 = 3<br \/>\nSo, (-2, 3) is the solution of the system.<\/p>\n<p><strong>Solve each system of equations by adding or subtracting.<\/strong><\/p>\n<p>Question 2.<br \/>\n\\(\\left\\{\\begin{array}{l}x+2y=-2 \\\\-3x+2y=-10\\end{array}\\right.\\)<br \/>\nx = ________<br \/>\ny = ________<\/p>\n<p>Answer:<br \/>\nx = 2<br \/>\ny = -2<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}x+2y=-2 \\\\-3x+2y=-10\\end{array}\\right.\\)<br \/>\nSubtract the equations<br \/>\nx + 2y = -2<br \/>\n-(-3x + 2y = -10)<br \/>\ny is eliminated as it has reversed coefficients. Solve for x<br \/>\nx + 2y + 3x &#8211; 2y = -2 + 10<br \/>\n4x = 8<br \/>\nx = 8\/4 = 2<br \/>\nSubstituting x in either of the equation to find y<br \/>\n2 + 2y = -2<br \/>\n2 + 2y -2 = -2 -2<br \/>\n2y = -4<br \/>\ny = -4\/2 = -2<br \/>\n(2, -2) is the answer.<\/p>\n<p>Question 3.<br \/>\n\\(\\left\\{\\begin{array}{l}3x+y=23 \\\\3x-2y=8\\end{array}\\right.\\)<br \/>\n(________ , ________)<\/p>\n<p>Answer:<br \/>\n(6, 5)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}3x+y=23 \\\\3x-2y=8\\end{array}\\right.\\)<br \/>\nSubtract the equations<br \/>\n3x + y = 23<br \/>\n-(3x &#8211; 2y = 8)<br \/>\nx is eliminated as it has reversed coefficients. Solve for y<br \/>\n3x + y &#8211; 3x + 2y = 23 &#8211; 8<br \/>\n3y = 15<br \/>\ny = 15\/3 = 5<br \/>\nSubstituting y in either of the equation to find x<br \/>\n3x + 5 = 23<br \/>\n3x + 5 &#8211; 5 = 23 &#8211; 5<br \/>\n3x = 18<br \/>\nx = 18\/3 = 6<br \/>\nSolution is (6, 5)<\/p>\n<p>Question 4.<br \/>\n\\(\\left\\{\\begin{array}{l}-4x-5y=7 \\\\3x+5y=-14\\end{array}\\right.\\)<br \/>\n(________ , ________)<\/p>\n<p>Answer:<br \/>\n(7, -7)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}-4x-5y=7 \\\\3x+5y=-14\\end{array}\\right.\\)<br \/>\nAdd the equations<br \/>\n-4x &#8211; 5y = 7<br \/>\n+(3x + 5y = -14)<br \/>\ny is eliminated as it has reversed coefficients. Solve for x<br \/>\n-4x -5y +3x + 5y = 7 -14<br \/>\n-x = -7<br \/>\nx = -7\/-1 = 7<br \/>\nSubstituting x in either of the equation to find y<br \/>\n3(7) + 5y = -14<br \/>\n21 + 5y -21 = -14 -21<br \/>\n5y = -35<br \/>\ny = -35\/5 = -7<br \/>\nThe answer is (7, -7)<\/p>\n<p>Question 5.<br \/>\n\\(\\left\\{\\begin{array}{l}x-2y=-19 \\\\5x+2y=1\\end{array}\\right.\\)<br \/>\n(________ , ________)<\/p>\n<p>Answer:<br \/>\n(-3, 8)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}x-2y=-19 \\\\5x+2y=1\\end{array}\\right.\\)<br \/>\nAdd the equations<br \/>\nx &#8211; 2y = -19<br \/>\n+(5x + 2y = 1)<br \/>\ny is eliminated as it has reversed coefficients. Solve for x<br \/>\nx &#8211; 2y + 5x + 2y = -19 + 1<br \/>\n6x = -18<br \/>\nx = -18\/6 = -3<br \/>\nSubstituting x in either of the equation to find y<br \/>\n-3 -2y = -19<br \/>\n-3 -2y + 3 = -19 + 3<br \/>\n-2y = -16<br \/>\ny = -16\/-2 = 8<br \/>\nThe answer is (-3, 8)<\/p>\n<p>Question 6.<br \/>\n\\(\\left\\{\\begin{array}{l}3x+4y=18 \\\\-2x+4y=8\\end{array}\\right.\\)<br \/>\n(________ , ________)<\/p>\n<p>Answer:<br \/>\n(2, 3)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}3x+4y=18 \\\\-2x+4y=8\\end{array}\\right.\\)<br \/>\nSubtract the equations<br \/>\n3x + 4y = 18<br \/>\n-(-2x + 4y = 8)<br \/>\ny is eliminated as it has reversed coefficients. Solve for x<br \/>\n3x + 4y + 2x &#8211; 4y = 18 &#8211; 8<br \/>\n5x = 10<br \/>\nx = 10\/5 = 2<br \/>\nSubstituting x in either of the equation to find y<br \/>\n3(2) + 4y = 18<br \/>\n6 + 4y &#8211; 6 = 18 &#8211; 6<br \/>\n4y = 12<br \/>\ny = 12\/4 =3<br \/>\nSolution is (2, 3)<\/p>\n<p>Question 7.<br \/>\n\\(\\left\\{\\begin{array}{l}-5x+7y=11 \\\\-5x+3y=19\\end{array}\\right.\\)<br \/>\n(________ , ________)<\/p>\n<p>Answer:<br \/>\n(-5, -2)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}-5x+7y=11 \\\\-5x+3y=19\\end{array}\\right.\\)<br \/>\nSubtract the equations<br \/>\n-5x + 7y = 11<br \/>\n-(-5x + 3y = 19)<br \/>\nx is eliminated as it has reversed coefficients. Solve for y<br \/>\n-5x + 7y + 5x &#8211; 3y = 11 &#8211; 19<br \/>\n4y = -8<br \/>\ny = -8\/4 = -2<br \/>\nSubstituting y in either of the equation to find x<br \/>\n-5x + 7(-2) = 11<br \/>\n-5x -14 + 14 = 11 + 14<br \/>\n-5x = 25<br \/>\nx = 25\/-5 = -5<br \/>\nSolution is (-5, -2)<\/p>\n<p>Question 8.<br \/>\nThe Green River Freeway has a minimum and a maximum speed limit. Tony drove for 2 hours at the minimum speed limit and 3.5 hours at the maximum limit, a distance of 355 miles. Rae drove 2 hours at the minimum speed limit and 3 hours at the maximum limit, a distance of 320 miles. What are the two speed limits?<br \/>\na. Write equatios to represent Tony\u2019s distance and Rae\u2019s distance.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nTony&#8217;s distance: 2x + 3.5y = 355<br \/>\nRae&#8217;s distance: 2x + 3y = 320<br \/>\nwhere x is the minimum speed and y is the maximum speed.<\/p>\n<p>Question 8.<br \/>\nb. Solve the system.<br \/>\nminimum speed limit:______________<br \/>\nmaximum speed limit______________<br \/>\nminimum speed limit: ________ mi\/h<br \/>\nmaximum speed limit: ________ mi\/h<\/p>\n<p>Answer:<br \/>\nminimum speed limit:55<br \/>\nmaximum speed limit70<br \/>\nminimum speed limit: 55mi\/h<br \/>\nmaximum speed limit: 70mi\/h<\/p>\n<p>Explanation:<br \/>\nSubtract the equations<br \/>\n2x + 3.5y = 355<br \/>\n-(2x + 3y = 320)<br \/>\nx is eliminated as it has reversed coefficients. Solve for y<br \/>\n2x + 3.5y &#8211; 2x &#8211; 3y = 355 &#8211; 320<br \/>\n0.5y = 35<br \/>\ny = 35\/0.5 = 70<br \/>\nSubstituting y in either of the equation to find x<br \/>\n2x + 3(70) = 320<br \/>\n2x + 210 &#8211; 210 = 320 &#8211; 210<br \/>\n2x = 110<br \/>\nx = 110\/2 = 55<br \/>\nMinimum speed limit: 55 miles per hour<br \/>\nMaximum speed limit: 70 miles per hour<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 9.<br \/>\nCan you use addition or subtraction to solve any system? Explain.<br \/>\n________<\/p>\n<p>Answer:<br \/>\nNo. One of the variables should have the same coefficient in order to add or subtract the system.<\/p>\n<h3><a id=\"Solving_Systems_by_Elimination_\u2013_Page_No._249\"><\/a>8.3 Independent Practice &#8211; Solving Systems by Elimination &#8211; Page No. 249<\/h3>\n<p>Question 10.<br \/>\nRepresent Real-World Problems Marta bought new fish for her home aquarium. She bought 3 guppies and 2 platies for a total of $13.95. Hank also bought guppies and platies for his aquarium. He bought 3 guppies and 4 platies for a total of $18.33. Find the price of a guppy and the price of a platy.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6627 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-13.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 3: Solving Systems by Elimination img 13\" width=\"257\" height=\"235\" \/><br \/>\nGuppy: $ ________<br \/>\nPlaty: $ ________<\/p>\n<p>Answer:<br \/>\nGuppy: $ 3.19<br \/>\nPlaty: $ 2.19<\/p>\n<p>Explanation:<br \/>\n3x + 2y = 13.95<br \/>\n3x + 4y = 18.33<br \/>\nwhere x is the unit price of guppy and y is the unit price of platy<br \/>\nSubtract the equations<br \/>\n3x + 2y = 13.95<br \/>\n-(3x + 4y = 18.33)<br \/>\nx is eliminated as it has reversed coefficients. Solve for y<br \/>\n3x + 2y &#8211; 3x &#8211; 4y = 13.95 &#8211; 18.33<br \/>\n-2y = -4.38<br \/>\ny = -4.38\/-2 = 2.19<br \/>\nSubstituting y in either of the equation to find x<br \/>\n3x + 2(2.19) = 13.95<br \/>\n3x + 4.38 &#8211; 4.38 = 13.95 &#8211; 4.38<br \/>\n3x = 9.57<br \/>\nx = 9.57\/3 = 3.19<br \/>\nThe price of a guppy is $3.19 and price of a platy is $2.19<\/p>\n<p>Question 11.<br \/>\nRepresent Real-World Problems The rule for the number of fish in a home aquarium is 1 gallon of water for each inch of fish length. Marta\u2019s aquarium holds 13 gallons and Hank\u2019s aquarium holds 17 gallons. Based on the number of fish they bought in Exercise 10, how long is a guppy and how long is a platy?<br \/>\nLength of a guppy = ________ inches<br \/>\nLength of a platy = ________ inches<\/p>\n<p>Answer:<br \/>\nLength of a guppy = 3 inches<br \/>\nLength of a platy = 2 inches<\/p>\n<p>Explanation:<br \/>\n3x + 2y = 13<br \/>\n3x + 4y = 17<br \/>\nwhere x is the length of guppy and y is the length of a platy<br \/>\nSubtract the equations<br \/>\n3x + 2y = 13<br \/>\n-(3x + 4y = 17)<br \/>\nx is eliminated as it has reversed coefficients. Solve for y<br \/>\n3x + 2y &#8211; 3x &#8211; 4y = 13 &#8211; 17<br \/>\n-2y = -4<br \/>\ny = -4\/-2 = 2<br \/>\nSubstituting y in either of the equation to find x<br \/>\n3x + 2(2) = 13<br \/>\n3x + 4 &#8211; 4 = 13 &#8211; 4<br \/>\n3x = 9<br \/>\nx = 9\/3 = 3<br \/>\nThe length of a guppy is 3 inches and price of a platy is 2 inches<\/p>\n<p>Question 12.<br \/>\nLine m passes through the points (6, 1) and (2, -3). Line n passes through the points (2, 3) and (5, -6). Find the point of intersection of these lines.<br \/>\nType below:<br \/>\n________________<\/p>\n<p>Answer:<br \/>\nThe intersection of these lines is (3.5, -1.5)<\/p>\n<p>Explanation:<br \/>\nFind the slope of line m = (y2 &#8211; y1)\/(x2 &#8211; x1) where (x2, y2) = (2, -3) and (x1, y1) = (6, 1)<br \/>\nSlope = (-3 -1)\/(2 &#8211; 6) = -4\/-4 = 1<br \/>\nSubstitute the value of m and any of the given ordered pair (x, y) in point-slope form of equation: y &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; 1 = 1(x &#8211; 6)<br \/>\ny &#8211; 1 = x &#8211; 6<br \/>\ny = x &#8211; 6 + 1<br \/>\nx &#8211; y = 5<br \/>\nFind the slope of line n = (y2 &#8211; y1)\/(x2 &#8211; x1) where (x2, y2) = (5, -6) and (x1, y1) = (2, 3)<br \/>\nSlope = (-6 -3)\/(5 &#8211; 2) = -9\/3 = -3<br \/>\nSubstitute the value of m and any of the given ordered pair (x, y) in point-slope form of equation: y &#8211; y1 = m(x &#8211; x1)<br \/>\ny &#8211; 3 = -3(x &#8211; 2)<br \/>\ny &#8211; 3 = -3x + 6<br \/>\ny = -3x + 6 + 3<br \/>\n3x + y = 9<br \/>\nAdd the equations<br \/>\nx &#8211; y = 5<br \/>\n+(3x + y = 9)<br \/>\ny is eliminated as it has reversed coefficients. Solve for x<br \/>\nx &#8211; y + 3x + y = 5 + 9<br \/>\n4x = 14<br \/>\nx = 14\/4 = 3.5<br \/>\nSubstituting x in either of the equation to find y<br \/>\n3.5 &#8211; y = 5<br \/>\n3.5 &#8211; y &#8211; 3.5 = 5 &#8211; 3.5<br \/>\n-y = 1.5<br \/>\ny = -1.5<br \/>\nThe intersection of these lines is (3.5, -1.5)<\/p>\n<p>Question 13.<br \/>\nRepresent Real-World Problems Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. The oil change for one car required 5 quarts of oil and cost $22.45. The oil change for the other car required 7 quarts of oil and cost $25.45. How much is the labor fee and how much is each quart of oil?<br \/>\nLabor fee: $ ________<br \/>\nQuart of oil: $ ________<\/p>\n<p>Answer:<br \/>\nLabor fee: $ 14.95<br \/>\nQuart of oil: $ 1.5<\/p>\n<p>Explanation:<br \/>\n5x + y = 22.45<br \/>\n7x + y = 25.45<br \/>\nwhere x is the unit cost of quarts of oil and y is the flat fee for labor<br \/>\nSubtract the equations<br \/>\n5x + y = 22.45<br \/>\n-(7x + y = 25.45)<br \/>\ny is eliminated as it has reversed coefficients. Solve for x<br \/>\n5x + y &#8211; 7x &#8211; y = 22.45 &#8211; 25.45<br \/>\n-2x = -3<br \/>\nx = -3\/-2 = 1.5<br \/>\nSubstituting x in either of the equation to find y<br \/>\n5(1.5) + y = 22.45<br \/>\n7.5 + y &#8211; 7.5 = 22.45 &#8211; 7.5<br \/>\ny = 14.95<br \/>\nLabor fee is $14.95 and unit cost of quart of oil is $1.5<\/p>\n<p>Question 14.<br \/>\nRepresent Real-World Problems A sales manager noticed that the number of units sold for two T-shirt styles, style A and style B, was the same during June and July. In June, total sales were $2779 for the two styles, with A selling for $15.95 per shirt and B selling for $22.95 per shirt. In July, total sales for the two styles were $2385.10, with A selling at the same price and B selling at a discount of 22% off the June price. How many T-shirts of each style were sold in June and July combined?<br \/>\n________ T-shirts of style A and style B were sold in June and July.<\/p>\n<p>Answer:<br \/>\n15.95x + 22.95y = 2779<br \/>\n15.95x + 17.9y = 2385.10<br \/>\nwhere x is number of style A shirt and y is the number of style B shirt<br \/>\nIn July, the price of style B shirt is 22% of the price of style B shirt in June, hence 0.78(22.95) = 17.90<br \/>\nSubtract the equations<br \/>\n15.95x + 22.95y = 2779<br \/>\n-(15.95x + 17.9y = 2385.10)<br \/>\nx is eliminated as it has reversed coefficients. Solve for y<br \/>\n15.95x + 22.95 &#8211; 15.95x &#8211; 17.9y = 2779 &#8211; 2385.10<br \/>\n5.05y = 393.9<br \/>\ny = 393.9\/5.05 = 78<br \/>\nSubstituting y in either of the equation to find x<br \/>\n15.95x +22.95(78) = 2779<br \/>\n15.95x + 1790.1 &#8211; 1790.1 = 2779 &#8211; 1790.1<br \/>\n15.95x = 988.9<br \/>\nx = 988.9\/15.95 = 62<br \/>\nThe number of style A T shirt sold in June is 62.<br \/>\nSince the number of T-shirts sold in both numbers is the same, the total number = 2. 62 = 124.<br \/>\nThe number of style B T-shirts sold in June is 78.<br \/>\nSince the number of T-shirts sold in both numbers is the same, the total number = 2. 78 = 156.<\/p>\n<p>Question 15.<br \/>\nRepresent Real-World Problems Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,874 was collected on the sale of 1,246 tickets. How many of each type of ticket were sold?<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6628 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-14.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 3: Solving Systems by Elimination img 14\" width=\"252\" height=\"185\" \/>img 14<br \/>\n________ adult tickets<br \/>\n________ student tickets<\/p>\n<p>Answer:<br \/>\n407 adult tickets<br \/>\n839 student tickets<\/p>\n<p>Explanation:<br \/>\nx + y = 1246<br \/>\n5x + y = 2874<br \/>\nwhere x is the number of adult tickets sold and y is the number of student tickets sold.<br \/>\nSubtract the equations<br \/>\nx + y = 1246<br \/>\n-(5x + y = 2874)<br \/>\ny is eliminated as it has reversed coefficients. Solve for x<br \/>\nx + y &#8211; 5x &#8211; y = 1246 &#8211; 2874<br \/>\n-4x = -1628<br \/>\nx = -1628\/-4 = 407<br \/>\nSubstituting x in either of the equation to find y<br \/>\n407 + y = 1246<br \/>\n407 + y &#8211; 407 = 1246 &#8211; 407<br \/>\ny = 839<br \/>\nThe number of adult tickets sold is 407 and student tickets sold is 839.<\/p>\n<h3><a id=\"Solving_Systems_by_Elimination_Lesson_Check_\u2013_Page_No._250\"><\/a>FOCUS ON HIGHER ORDER THINKING &#8211; Solving Systems by Elimination &#8211; Page No. 250<\/h3>\n<p>Question 16.<br \/>\nCommunicate Mathematical Ideas Is it possible to solve the system<br \/>\n\\(\\left\\{\\begin{array}{l}3x-2y=10 \\\\x+2y=6\\end{array}\\right.\\)<br \/>\nby using substitution? If so, explain how. Which method, substitution or elimination, is more efficient? Why?<br \/>\n________<\/p>\n<p>Answer:<br \/>\nThe system can be solved by substitution as x in equation 2 can be isolated.<br \/>\n3x &#8211; 2y = 10<br \/>\nx + 2y = 6<br \/>\nSolve the equation for x in the equation.<br \/>\nx = -2y + 6<br \/>\nSubstitute the expression for x in the other equation and solve.<br \/>\n3(-2y + 6) -2y = 10<br \/>\n-6y + 18 &#8211; 2y = 10<br \/>\n-8y + 18 = 10<br \/>\n-8y = -8<br \/>\ny = -8\/-8 = 1<br \/>\nSubstitute the values of y into one of the equations and solve for the other variable x.<br \/>\nx + 2(1) = 6<br \/>\nx = 4<br \/>\nThe solution is (4, 1)<br \/>\nAs the cofficient if variable y is opposite, it will be eliminated and solved for x in less number of steps.<br \/>\nElimination would be more efficient.<\/p>\n<p>Question 17.<br \/>\nJenny used substitution to solve the system<br \/>\n\\(\\left\\{\\begin{array}{l}2x+y=8 \\\\x-y=1\\end{array}\\right.\\). Her solution is shown below.<br \/>\nStep 1: y = -2x + 8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Solve the first equation for y.<br \/>\nStep 2: 2x + (-2x + 8) = 8\u00a0 \u00a0 \u00a0Substitute the value of y in an original equation.<br \/>\nStep 3: 2x &#8211; 2x + 8 = 8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 Use the Distributive Property.<br \/>\nStep 4: 8 = 8\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Simplify.<br \/>\na. Explain the Error Explain the error Jenny made. Describe how to correct it.<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n2x + y = 8<br \/>\nx &#8211; y = 1<br \/>\nRewritten equation should be substituted in the other original equation<br \/>\nError is that Jenny solved for y in the first equation and substitute it in the original equation.<br \/>\nx &#8211; (-2x + 8) = 1<br \/>\n3x &#8211; 8 = 1<br \/>\n3x = 9<br \/>\nx = 9\/3 = 3<br \/>\nx = 3<\/p>\n<p>Question 17.<br \/>\nb. Communicate Mathematical Ideas Would adding the equations have been a better method for solving the system? If so, explain why.<br \/>\n________<\/p>\n<p>Answer:<br \/>\nYes<\/p>\n<p>Explanation:<br \/>\nAs the coefficient, if variable y is the opposite, it will be eliminated and solved for x in less number of steps.<\/p>\n<h3><a id=\"Solving_Systems_by_Elimination_with_Multiplication_\u2013_Page_No._256\"><\/a>Guided Practice &#8211; Solving Systems by Elimination with Multiplication &#8211; Page No. 256<\/h3>\n<p>Question 1.<br \/>\nSolve the system<br \/>\n\\(\\left\\{\\begin{array}{l}3x-y=8 \\\\-2x+4y=-12\\end{array}\\right.\\)<br \/>\nby multiplying and adding.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6629 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-15.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 4: Solving Systems by Elimination with Multiplication img 15\" width=\"663\" height=\"351\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-15.jpg 663w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-15-300x159.jpg 300w\" sizes=\"(max-width: 663px) 100vw, 663px\" \/><br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\n\\(\\left\\{\\begin{array}{l}3x-y=8 \\\\-2x+4y=-12\\end{array}\\right.\\)<br \/>\nMultiply each term in the first equation by 4 to get opposite coefficients for the y-terms.<br \/>\n4(3x &#8211; y = 8)<br \/>\n12x &#8211; 4y = 32<br \/>\nAdd the second equation to the new equation<br \/>\n12x &#8211; 4y = 32<br \/>\n+(-2x + 4y = -12)<br \/>\nAdd to eliminate the variable y<br \/>\n10x = 20<br \/>\nDivide both sides by 10<br \/>\nx = 20\/10 = 2<br \/>\nSubstitue into one of the original equations and solve for y<br \/>\ny = 3(2) &#8211; 8 = -1<br \/>\nS0, (2, -2)is the solution of the system.<\/p>\n<p><strong>Solve each system of equations by multiplying first.<\/strong><\/p>\n<p>Question 2.<br \/>\n\\(\\left\\{\\begin{array}{l}x+4y=2 \\\\2x+5y=7\\end{array}\\right.\\)<br \/>\n(________ , ________ )<\/p>\n<p>Answer:<br \/>\n(6, -1)<\/p>\n<p>Explanation:<br \/>\nx + 4y = 2<br \/>\n2x + 5y = 7<br \/>\nTo eliminate x terms, multiply the 2nd equation by 2<br \/>\n2(x + 4y = 2)<br \/>\n2x + 8y = 4<br \/>\nSubtract the equations<br \/>\n2x + 8y = 4<br \/>\n-(2x + 5y = 7)<br \/>\nx is eliminated as it has reversed coefficients. Solve for y<br \/>\n2x + 8y &#8211; 2x &#8211; 5y = 4 &#8211; 7<br \/>\n3y = -3<br \/>\ny = -3\/3 = -1<br \/>\nSubstituting y in either of the equation to find x<br \/>\nx + 4(-1) = 2<br \/>\nx &#8211; 4 + 4 = 2 + 4<br \/>\nx = 6<br \/>\nSolution: (6, -1)<\/p>\n<p>Question 3.<br \/>\n\\(\\left\\{\\begin{array}{l}3x+y=-1 \\\\2x+3y=18\\end{array}\\right.\\)<br \/>\n(________ , ________ )<\/p>\n<p>Answer:<br \/>\n(-3, 8)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}3x+y=-1 \\\\2x+3y=18\\end{array}\\right.\\)<br \/>\nTo eliminate y terms, multiply the 1st equation by 3<br \/>\n3(3x + y = -1)<br \/>\n9x + 3y = -3<br \/>\nSubtract the equations<br \/>\n9x + 3y = -3<br \/>\n-(2x + 3y = 18)<br \/>\ny is eliminated as it has reversed coefficients. Solve for x<br \/>\n9x + 3y &#8211; 2x &#8211; 3y = -3 -18<br \/>\n7x = -21<br \/>\nx = -21\/7<br \/>\nx = -3<br \/>\nSubstituting x in either of the equation to find y<br \/>\n3(-3) + y = -1<br \/>\n-9 + y + 9 = -1 + 9<br \/>\ny = 8<br \/>\nSolution: (-3, 8)<\/p>\n<p>Question 4.<br \/>\n\\(\\left\\{\\begin{array}{l}2x+8y=21 \\\\6x-4y=14\\end{array}\\right.\\)<br \/>\nType below:<br \/>\n______________<\/p>\n<p>Answer:<br \/>\nThe soultion is (3.5, 1.75)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}2x+8y=21 \\\\6x-4y=14\\end{array}\\right.\\)<br \/>\nTo eliminate y terms, multiply the 2nd equation by 2<br \/>\n2(6x &#8211; 4y = 14)<br \/>\n2x + 8y = 21<br \/>\nAdd the equations<br \/>\n2x + 8y = 21<br \/>\n+(12x &#8211; 8y = 28)<br \/>\ny is eliminated it has reversed coefficients. Solve for x<br \/>\n2x + 8y + 12x &#8211; 8y = 21 + 28<br \/>\n14x = 49<br \/>\nx = 49\/14 = 3.5<br \/>\nSubstituting x in either of the equation to find y<br \/>\n6(3.5) &#8211; 4y = 14<br \/>\n21 &#8211; 4y &#8211; 21 = 14 &#8211; 21<br \/>\n-4y = -7<br \/>\ny = -7\/-4 = 1.75<br \/>\nThe soultion is (3.5, 1.75)<\/p>\n<p>Question 5.<br \/>\n\\(\\left\\{\\begin{array}{l}2x+y=3 \\\\-x+3y=-12\\end{array}\\right.\\)<br \/>\n(________ , ________ )<\/p>\n<p>Answer:<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}2x+y=3 \\\\-x+3y=-12\\end{array}\\right.\\)<br \/>\nTo eliminate x terms, multiply the 2nd equation by 2<br \/>\n2(-x + 3y = -12)<br \/>\n-2x + 6y = -24<br \/>\nAdd the equations<br \/>\n2x + y = 3<br \/>\n+(-2x + 6y = -24)<br \/>\nx is eliminated it has reversed coefficients. Solve for y<br \/>\n2x + y &#8211; 2x + 6y = 3 &#8211; 24<br \/>\n7y = -21<br \/>\ny = -21\/7 = -3<br \/>\nSubstituting y in either of the equation to find x<br \/>\n-x + 3(-3) = -12<br \/>\n-x -9 + 9 = -12 + 9<br \/>\n-x = -3<br \/>\nx = 3<br \/>\nThe soultion is (3, -3)<\/p>\n<p>Question 6.<br \/>\n\\(\\left\\{\\begin{array}{l}6x+5y=19 \\\\2x+3y=5\\end{array}\\right.\\)<br \/>\n(________ , ________ )<\/p>\n<p>Answer:<br \/>\nThe soultion is (4, -1)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}6x+5y=19 \\\\2x+3y=5\\end{array}\\right.\\)<br \/>\nTo eliminate x terms, multiply the 2nd equation by 3<br \/>\n3(2x + 3y = 5)<br \/>\n6x + 9y = 15<br \/>\nSubtract the equations<br \/>\n6x + 5y = 19<br \/>\n-(6x + 9y = 15)<br \/>\nx is eliminated it has reversed coefficients. Solve for y<br \/>\n6x + 5y &#8211; 6x &#8211; 9y = 19 &#8211; 15<br \/>\n-4y = 4<br \/>\ny = 4\/-4 = -1<br \/>\nSubstituting y in either of the equation to find x<br \/>\n2x + 3(-1) = 5<br \/>\n2x &#8211; 3 + 3 = 5 + 3<br \/>\n2x = 8<br \/>\nx = 8\/2 = 4<br \/>\nThe soultion is (4, -1)<\/p>\n<p>Question 7.<br \/>\n\\(\\left\\{\\begin{array}{l}2x+5y=16 \\\\-4x+3y=20\\end{array}\\right.\\)<br \/>\n(________ , ________ )<\/p>\n<p>Answer:<br \/>\nThe soultion is (-2, 4)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}2x+5y=16 \\\\-4x+3y=20\\end{array}\\right.\\)<br \/>\nTo eliminate x terms, multiply the 1st equation by 2<br \/>\n2(2x + 5y = 16)<br \/>\n4x + 10y = 32<br \/>\nAdd the equations<br \/>\n4x + 10y = 32<br \/>\n+(-4x + 3y = 20)<br \/>\nx is eliminated it has reversed coefficients. Solve for y<br \/>\n10y + 3y = 32 + 20<br \/>\n13y = 52<br \/>\ny = 52\/13 = 4<br \/>\nSubstituting y in either of the equation to find x<br \/>\n2x + 5(4) = 16<br \/>\n2x + 20 &#8211; 20 = 16 &#8211; 20<br \/>\n2x = -4<br \/>\nx = -4\/2 = -2<br \/>\nThe soultion is (-2, 4)<\/p>\n<p>Question 8.<br \/>\nBryce spent $5.26 on some apples priced at $0.64 each and some pears priced at $0.45 each. At another store he could have bought the same number of apples at $0.32 each and the same number of pears at $0.39 each, for a total cost of $3.62. How many apples and how many pears did Bryce buy?<br \/>\na. Write equations to represent Bryce\u2019s expenditures at each store<br \/>\nFirst store: _____________<br \/>\nSecond store: _____________<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nFirst store: 0.64x + 0.45y = 5.26<br \/>\nSecond store: 0.32x + 0.39y = 3.62<\/p>\n<p>Explanation:<br \/>\nFirst store = 0.64x + 0.45y = 5.26<br \/>\nSecond store = 0.32x + 0.39y = 3.62<br \/>\nwhere x is the number of apples and y is the number of pears.<\/p>\n<p>Question 8.<br \/>\nb. Solve the system.<br \/>\nNumber of apples: _______<br \/>\nNumber of pears: _______<\/p>\n<p>Answer:<br \/>\nNumber of apples: 4<br \/>\nNumber of pears: 6<\/p>\n<p>Explanation:<br \/>\nFirst store = 0.64x + 0.45y = 5.26<br \/>\nSecond store = 0.32x + 0.39y = 3.62<br \/>\nMultiply by 100<br \/>\n64x + 45y = 526<br \/>\n32x + 39y = 362<br \/>\nTo eliminate x terms, multiply the 2nd equation by 2<br \/>\n2(32x + 39y = 362)<br \/>\n64x + 45y = 526<br \/>\nSubtract the equations<br \/>\n64x + 45y = 526<br \/>\n-(64x + 78y = 724)<br \/>\nx is eliminated it has reversed coefficients. Solve for y<br \/>\n64x + 45y &#8211; 64x &#8211; 78y = 526 &#8211; 724<br \/>\n-33y = -198<br \/>\ny = -198\/-33 = 6<br \/>\nSubstituting y in either of the equation to find x<br \/>\n32x + 39(6) = 362<br \/>\n32x + 234 &#8211; 234 = 362 &#8211; 234<br \/>\n32x = 128<br \/>\nx = 128\/32 = 4<br \/>\nHe bought 4 apples and 6 pears.<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 9.<br \/>\nWhen solving a system by multiplying and then adding or subtracting, how do you decide whether to add or subtract?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nIf the variable with the same coefficient but reversed sign, we add and if they have the same sign, we subtract.<\/p>\n<h3><a id=\"Solving_Systems_by_Elimination_with_Multiplication_\u2013_Page_No._257\"><\/a>Solving Systems by Elimination with Multiplication &#8211; Page No. 257<\/h3>\n<p>Question 10.<br \/>\nExplain the Error Gwen used elimination with multiplication to solve the system<br \/>\n\\(\\left\\{\\begin{array}{l}2x+6y=3 \\\\x-3y=-1\\end{array}\\right.\\)<br \/>\nHer work to find x is shown. Explain her error. Then solve the system.<br \/>\n2(x \u2212 3y) = -1<br \/>\n2x \u2212 6y = -1<br \/>\n+2x + 6y = 3<br \/>\n_____________<br \/>\n4x + 0y = 2<br \/>\nx = \\(\\frac{1}{2}\\)<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\n2x + 6y = 3<br \/>\nx &#8211; 3y = -1<br \/>\nTo eliminate x terms, multiply the 2nd equation by 2<br \/>\n2(x &#8211; 3y = -1)<br \/>\n2x &#8211; 6y = -2<br \/>\nError is the Gnew did not multiply the entire expression with 2.<br \/>\nAdd the equations<br \/>\n2x + 6y = 3<br \/>\n+(2x &#8211; 6y = -2)<br \/>\ny is eliminated it has reversed coefficients. Solve for x<br \/>\n2x + 6y + 2x &#8211; 6y = 3 &#8211; 2<br \/>\n4x = 1<br \/>\nx = 1\/4<br \/>\nSubstituting x in either of the equation to find y<br \/>\nx &#8211; 3y = -1<br \/>\n1\/4 &#8211; 3y &#8211; 1\/4 = -1 -1\/4<br \/>\n-3y = -5\/4<br \/>\ny = -5\/4(-3) = 5\/12<\/p>\n<p>Question 11.<br \/>\nRepresent Real-World Problems At Raging River Sports, polyester-fill sleeping bags sell for $79. Down-fill sleeping bags sell for $149. In one week the store sold 14 sleeping bags for $1,456.<br \/>\na. Let x represent the number of polyester-fill bags sold and let y represent the number of down-fill bags sold. Write a system of equations you can solve to find the number of each type sold.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6630 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-16.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 4: Solving Systems by Elimination with Multiplication img 16\" width=\"333\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-16.jpg 333w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-16-300x214.jpg 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nx + y = 14<br \/>\n79x + 149y = 1456<br \/>\nwhere x is the polyster-fill bags and y is the number of down-fill bags<\/p>\n<p>Question 11.<br \/>\nb. Explain how you can solve the system for y by multiplying and subtracting.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nx + y = 14<br \/>\n79x + 149y = 1456<br \/>\nMultiply the second equation by 79. Subtract the new equation from the first equation and solve the resulting equation for y.<\/p>\n<p>Question 11.<br \/>\nc. Explain how you can solve the system for y using substitution.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nSolve the second equation for x. Substitute the expression for x , in the first equation and solve the resulting equation for y.<\/p>\n<p>Question 11.<br \/>\nd. How many of each type of bag were sold?<br \/>\n_______ polyester-fill<br \/>\n_______ down-fill<\/p>\n<p>Answer:<br \/>\n9 polyester-fill<br \/>\n5 down-fill<\/p>\n<p>Explanation:<br \/>\nx + y = 14<br \/>\n79x + 149y = 1456<br \/>\nTo eliminate x terms, multiply the 2nd equation by 2<br \/>\n79(x + y = 14)<br \/>\n79x + 149y = 1456<br \/>\nSubtract the equations<br \/>\n79x + 79y = 1106<br \/>\n-(79x + 149y = 1456)<br \/>\nx is eliminated it has reversed coefficients. Solve for y<br \/>\n79x + 79y &#8211; 79x &#8211; 149y = 1106 &#8211; 1456<br \/>\n-70y = -350<br \/>\ny = -350\/-70 = 5<br \/>\nSubstituting y in either of the equation to find x<br \/>\nx + 5 = 14<br \/>\nx = 14 &#8211; 5<br \/>\nx = 9<br \/>\nThere were 9 polyster-fill bags and 5 down-fill bags sold.<\/p>\n<p>Question 12.<br \/>\nTwice a number plus twice a second number is 310. The difference between the numbers is 55. Find the numbers by writing and solving a system of equations. Explain how you solved the system.<br \/>\nx = _______<br \/>\ny = _______<\/p>\n<p>Answer:<br \/>\nx = 105<br \/>\ny = 50<\/p>\n<p>Explanation:<br \/>\n2x + 2y = 310<br \/>\nx &#8211; y = 55<br \/>\nTo eliminate y terms, multiply the 2nd equation by 2<br \/>\n2(x &#8211; y = 55)<br \/>\n2x &#8211; 2y = 110<br \/>\nAdd the equations<br \/>\n2x + 2y = 310<br \/>\n+ (2x &#8211; 2y = 110)<br \/>\ny is eliminated it has reversed coefficients. Solve for x<br \/>\n2x + 2y + 2x &#8211; 2y = 310 + 110<br \/>\n4x = 420<br \/>\nx = 420\/4 = 105<br \/>\nSubstituting x in either of the equation to find y<br \/>\n105 &#8211; y = 55<br \/>\ny = 105 &#8211; 55<br \/>\ny = 50<br \/>\nThe solution is (105, 50)<\/p>\n<h3><a id=\"Solving_Systems_by_Elimination_with_Multiplication_Lesson_Check_\u2013_Page_No._258\"><\/a>Solving Systems by Elimination with Multiplication &#8211; Page No. 258<\/h3>\n<p>Question 13.<br \/>\nRepresent Real-World Problems A farm stand sells apple pies and jars of applesauce. The table shows the number of apples needed to make a pie and a jar of applesauce. Yesterday, the farm picked 169 Granny Smith apples and 95 Red Delicious apples. How many pies and jars of applesauce can the farm make if every apple is used?<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6631 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-17.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 4: Solving Systems by Elimination with Multiplication img 17\" width=\"691\" height=\"237\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-17.jpg 691w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-17-300x103.jpg 300w\" sizes=\"(max-width: 691px) 100vw, 691px\" \/><br \/>\n_______ pies<br \/>\n_______ jars of applesauce<\/p>\n<p>Answer:<br \/>\n21 pies<br \/>\n16 jars of applesauce<\/p>\n<p>Explanation:<br \/>\n5x + 4y = 169<br \/>\n3x + 2y = 95<br \/>\nwhere x is the number of apples needed for pie and y is the number of apples for jar of applesauce<br \/>\nTo eliminate y terms, multiply the 2nd equation by 2<br \/>\n2(3x + 2y = 95)<br \/>\n6x + 4y = 190<br \/>\nSubtract the equations<br \/>\n5x + 4y = 169<br \/>\n&#8211; (6x + 4y = 190)<br \/>\ny is eliminated it has reversed coefficients. Solve for x<br \/>\n5x + 4y &#8211; 6x &#8211; 4y = 169 &#8211; 190<br \/>\n-x = -21<br \/>\nx = -21\/-1 = 21<br \/>\nSubstituting x in either of the equation to find y<br \/>\n5(21) + 4y = 169<br \/>\n105 + 4y &#8211; 105 = 169 &#8211; 105<br \/>\n4y = 64<br \/>\ny = 64\/4 = 16<br \/>\nThe number of apples needed for pie is 21 and the number of apples for jar of applesauce is 16.<\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 14.<br \/>\nMake a Conjecture Lena tried to solve a system of linear equations algebraically and in the process found the equation 5 = 9. Lena thought something was wrong, so she graphed the equations and found that they were parallel lines. Explain what Lena\u2019s graph and equation could mean.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nLena&#8217;s graph is a parallel line which means the graph does not intersect each other, hence they have no solutions. Equation 5 = 9 means variables are eliminated and this statement is not true. This linear system has no solution.<\/p>\n<p>Question 15.<br \/>\nConsider the system<br \/>\n\\(\\left\\{\\begin{array}{l}2x+3y=6 \\\\3x+7y=-1\\end{array}\\right.\\)<br \/>\na. Communicate Mathematical Ideas Describe how to solve the system by multiplying the first equation by a constant and subtracting. Why would this method be less than ideal?<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nMultiplying the first equation by a constant and subtracting<br \/>\n2x + 3y = 6<br \/>\n3x + 7y = -1<br \/>\nMultiply the first equation by 1.5 and subtract. This would be less than ideal because you would introduce decimals into the solution process.<\/p>\n<p>Question 15.<br \/>\nb. Draw Conclusions Is it possible to solve the system by multiplying both equations by integer constants? If so, explain how.<br \/>\nType below:<br \/>\n____________<\/p>\n<p>Answer:<br \/>\nYes<\/p>\n<p>Explanation:<br \/>\nMultiply the first equation by 3 and the second equation by 2. Both x-term coefficients would be 6. Solve by eliminating the x-terms using subtraction.<\/p>\n<p>Question 15.<br \/>\nc. Use your answer from part b to solve the system.<br \/>\n(_______ , _______)<\/p>\n<p>Answer:<br \/>\n(9, -4)<\/p>\n<p>Explanation:<br \/>\n2x + 3y = 6<br \/>\n3x + 7y = -1<br \/>\nMultiply the first equation by 3 and the second equation by 2.<br \/>\n3(2x + 3y = 6)<br \/>\n2(3x + 7y = -1)<br \/>\nSubtract the equations<br \/>\n6x + 9y = 18<br \/>\n-(6x + 14y = -2)<br \/>\nx is eliminated it has reversed coefficients. Solve for y<br \/>\n6x + 9y &#8211; 6x &#8211; 14y = 18 + 2<br \/>\n-5y = 20<br \/>\ny = 20\/-5 = -4<br \/>\nSubstituting y in either of the equation to find x<br \/>\n2x + 3(-4) = 6<br \/>\n2x = 18<br \/>\nx = 18\/2 = 9<br \/>\nThe solution is (9, -4)<\/p>\n<h3><a id=\"Solving_Solving_Special_Systems_\u2013_Page_No._262\"><\/a>Guided Practice &#8211; Solving Solving Special Systems &#8211; Page No. 262<\/h3>\n<p><strong>Use the graph to solve each system of linear equations<\/strong><\/p>\n<p>Question 1.<br \/>\nA. \\(\\left\\{\\begin{array}{l}4x-2y=-6 \\\\2x-y=4\\end{array}\\right.\\)<br \/>\nB. \\(\\left\\{\\begin{array}{l}4x-2y=-6 \\\\x+y=6\\end{array}\\right.\\)<br \/>\nC. \\(\\left\\{\\begin{array}{l}2x-y=4 \\\\6x-3y=-12\\end{array}\\right.\\)<br \/>\nSTEP 1 Decide if the graphs of the equations in each system intersect, are parallel, or are the same line.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6632 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-18.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 5: Solving Solving Special Systems img 18\" width=\"257\" height=\"260\" \/><br \/>\nSystem A: The graphs __________<br \/>\nSystem B: The graphs __________<br \/>\nSystem C: The graphs __________<\/p>\n<p>Answer:<br \/>\nSystem A: The graphs are parallel<br \/>\nSystem B: The graphs are intersecting<br \/>\nSystem C: The graphs are\u00a0 the same line<\/p>\n<p>Explanation:<br \/>\nSystem A: 4x &#8211; 2y = -6<br \/>\n2x &#8211; y = 4<br \/>\nSystem B: 4x &#8211; 2y = -6<br \/>\nx + y = 6<br \/>\nSystem C: 2x &#8211; y = 4<br \/>\n6x &#8211; 3y = 12<\/p>\n<p>Question 1.<br \/>\nSTEP 2 Decide how many points the graphs have in common.<br \/>\na. Intersecting lines have _______________ point(s) in common.<br \/>\nb. Parallel lines have _______________ point(s) in common.<br \/>\nc. The same lines have ___________ point(s) in common.<br \/>\na. __________<br \/>\nb. __________<br \/>\nc. __________<\/p>\n<p>Answer:<br \/>\na. Intersecting lines have one point(s) in common.<br \/>\nb. Parallel lines have no point(s) in common.<br \/>\nc. The same lines have infinitely many points (s) in common.<\/p>\n<p>Explanation:<br \/>\nFrom the graphs,<br \/>\nIntersecting lines have one point(s) in common<br \/>\nParallel lines have no point(s) in common<br \/>\nThe same lines have infinitely many points (s) in common<\/p>\n<p>Question 1.<br \/>\nSTEP 3 Solve each system.<br \/>\nSystem A has __________ points in common, so it has __________ solution.<br \/>\nSystem B has __________ point in common. That point is the solution, __________.<br \/>\nSystem C has __________ points in common. ________ ordered pairs on the line will make both equations true.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nSystem A has no points in common, so it has no solution. System B has one point in common. That point is the solution, (1,5). System C has an infinite number of points in common. All ordered pairs on the line will make both equations true.<\/p>\n<p>Explanation:<br \/>\nNumber of solutions for each system<br \/>\nSystem A has no points in common, so it has no solution. System B has one point in common. That point is the solution, (1,5). System C has an infinite number of points in common. All ordered pairs on the line will make both equations true.<\/p>\n<p><strong>Solve each system. Tell how many solutions each system has.<\/strong><\/p>\n<p>Question 2.<br \/>\n\\(\\left\\{\\begin{array}{l}x-3y=4 \\\\-5x+15y=-20\\end{array}\\right.\\)<br \/>\n___________<\/p>\n<p>Answer:<br \/>\ninfinitely many solutions<\/p>\n<p>Explanation:<br \/>\nx &#8211; 3y = 4<br \/>\n-5x + 15y = -20<br \/>\nTo eliminate y terms, multiply the 1st equation by 5<br \/>\n5(x &#8211; 3y = 4)<br \/>\n5x &#8211; 15y = 20<br \/>\nAdd the equations<br \/>\n5x &#8211; 15y = 20<br \/>\n+(-5x + 15y = -20)<br \/>\nx and y is eliminated as it has reversed coefficients.<br \/>\n5x &#8211; 15y &#8211; 5x + 15y = 20 &#8211; 20<br \/>\n0 = 0<br \/>\nThe statement is true, hence the solution has infinitely many solutions.<\/p>\n<p>Question 3.<br \/>\n\\(\\left\\{\\begin{array}{l}6x+2y=-4 \\\\3x+y=4\\end{array}\\right.\\)<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nno solution<\/p>\n<p>Explanation:<br \/>\n6x + 2y = -4<br \/>\n3x + y = 4<br \/>\nTo eliminate y terms, multiply the 2nd equation by 5<br \/>\n2(3x + y = 4)<br \/>\n6x + 2y = 8<br \/>\nSubtract the equations<br \/>\n6x + 2y = -4<br \/>\n-(6x + 2y = 8)<br \/>\nx and y is eliminated as it has reversed coefficients.<br \/>\n6x + 2y &#8211; 6x &#8211; 2y = -4 -8<br \/>\n0 = -12<br \/>\nThe statement is false, hence the solution has no solution.<\/p>\n<p>Question 4.<br \/>\n\\(\\left\\{\\begin{array}{l}6x-2y=-10 \\\\3x+4y=-25\\end{array}\\right.\\)<br \/>\n___________<\/p>\n<p>Answer:<br \/>\none solution<\/p>\n<p>Explanation:<br \/>\n6x &#8211; 2y = -10<br \/>\n3x + 4y = -25<br \/>\nTo eliminate y terms, multiply the 1st equation by 2<br \/>\n2(6x &#8211; 2y = -10)<br \/>\n12x &#8211; 4y = -20<br \/>\nAdd the equations<br \/>\n12x &#8211; 4y = -20<br \/>\n+(3x + 4y = -25)<br \/>\ny is eliminated as it has reversed coefficients. Solve for x.<br \/>\n12x &#8211; 4y + 3x + 4y = -20 &#8211; 25<br \/>\n15x = -45<br \/>\nx = -45\/15 = -3<br \/>\nSubstitute x in any one of the original equations and solve for y<br \/>\n3(-3) + 4y = -25<br \/>\n-9 + 4y + 9 = -25 + 9<br \/>\n4y = -16<br \/>\ny = -16\/4<br \/>\ny = -4<br \/>\nThere is one solution, (-3, -4)<\/p>\n<p><strong>ESSENTIAL QUESTION CHECK-IN<\/strong><\/p>\n<p>Question 5.<br \/>\nWhen you solve a system of equations algebraically, how can you tell whether the system has zero, one, or an infinite number of solutions?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nWhen x and y are eliminated and the statement is true, the system has infinitely many solutions.<br \/>\nWhen x and y are eliminated and the statement is false, the system has no solutions.<br \/>\nWhen the system has one solution by solving, the system has one solution.<\/p>\n<h3><a id=\"Solving_Solving_Special_Systems_\u2013_Page_No._263\"><\/a>8.5 Independent Practice &#8211; Solving Solving Special Systems &#8211; Page No. 263<\/h3>\n<p><strong>Solve each system by graphing. Check your answer algebraically.<\/strong><\/p>\n<p>Question 6.<br \/>\n\\(\\left\\{\\begin{array}{l}-2x+6y=12 \\\\x-3y=3\\end{array}\\right.\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6633 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-19.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 5: Solving Solving Special Systems img 19\" width=\"222\" height=\"216\" \/><br \/>\nSolution: ______________<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n\\(\\left\\{\\begin{array}{l}-2x+6y=12 \\\\x-3y=3\\end{array}\\right.\\)<br \/>\nGraph the equations on same coordinate plane<br \/>\nNo solution as equations are parallel<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-1-1-300x248.png\" alt=\"grade 8 chapter 8 image 1\" width=\"300\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-1-1-300x248.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-1-1.png 506w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nTo eliminate y terms, multiply the 2nd equation by 2<br \/>\n2(x &#8211; 3y = 3)<br \/>\n2x &#8211; 6y = 6<br \/>\nAdd the equations<br \/>\n-2x + 6y = 12<br \/>\n2x &#8211; 6y = 6<br \/>\nx and y is eliminated as it has reversed coefficients.<br \/>\n-2x + 6y + 2x &#8211; 6y = 12 + 6<br \/>\n0 = 18<br \/>\nThe statement is false, hence the system has no solution.<\/p>\n<p>Question 7.<br \/>\n\\(\\left\\{\\begin{array}{l}15x+5y=5 \\\\3x+y=1\\end{array}\\right.\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6634 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-20.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 5: Solving Solving Special Systems img 20\" width=\"218\" height=\"221\" \/><br \/>\nSolution: ______________<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n\\(\\left\\{\\begin{array}{l}15x+5y=5 \\\\3x+y=1\\end{array}\\right.\\)<br \/>\nGraph the equations on same coordinate plane<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-2-1-265x300.png\" alt=\"grade 8 chapter 8 image 2\" width=\"265\" height=\"300\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-2-1-265x300.png 265w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-2-1.png 446w\" sizes=\"(max-width: 265px) 100vw, 265px\" \/><br \/>\nInfinitely many solutions as equations are overlapping<br \/>\nTo eliminate y terms, multiply the 2nd equation by 5<br \/>\n5(3x + y = 1)<br \/>\n15x + 5y = 5<br \/>\nSubtarct the equations<br \/>\n15x + 5y = 5<br \/>\n-(15x + 5y = 5)<br \/>\nx and y is eliminated as it has reversed coefficients.<br \/>\n15x + 5y -15x &#8211; 5y = 5 &#8211; 5<br \/>\n0 = 0<br \/>\nThe statement is true, hence the system has infinitely many solutions.<\/p>\n<p><strong>For Exs. 8\u2013<\/strong><\/p>\n<p><strong>14, state the number of solutions for each system of linear equations<\/strong><\/p>\n<p>Question 8.<br \/>\na system whose graphs have the same slope but different y-intercepts<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nNo solutions<\/p>\n<p>Explanation:<br \/>\nEquations are parallel<br \/>\nNo solutions<\/p>\n<p>Question 9.<br \/>\na system whose graphs have the same y-intercepts but different slopes<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nOne solution<\/p>\n<p>Explanation:<br \/>\nEquations are intersecting<br \/>\nOne solution<\/p>\n<p>Question 10.<br \/>\na system whose graphs have the same y-intercepts and the same slopes<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nInfinitely many solutions<\/p>\n<p>Explanation:<br \/>\nEquations are overlapping<br \/>\nInfinitely many solutions<\/p>\n<p>Question 11.<br \/>\na system whose graphs have different y-intercepts and different slopes<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nOne solution<\/p>\n<p>Explanation:<br \/>\nEquations are intersecting<br \/>\nOne solution<\/p>\n<p>Question 12.<br \/>\nthe system<br \/>\n\\(\\left\\{\\begin{array}{l}y=2 \\\\y=-3\\end{array}\\right.\\)<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nNo solutions<\/p>\n<p>Explanation:<br \/>\nEquations are parallel<br \/>\nNo solutions<\/p>\n<p>Question 13.<br \/>\nthe system<br \/>\n\\(\\left\\{\\begin{array}{l}y=2 \\\\y=-3\\end{array}\\right.\\)<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nOne solution<\/p>\n<p>Explanation:<br \/>\nEquations are intersecting<br \/>\nOne solution<\/p>\n<p>Question 14.<br \/>\nthe system whose graphs were drawn using these tables of values:<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6635 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-21.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 5: Solving Solving Special Systems img 21\" width=\"594\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-21.jpg 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-21-300x48.jpg 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><br \/>\n___________<\/p>\n<p>Answer:<br \/>\nNo solutions<\/p>\n<p>Explanation:<br \/>\nEquations are parallel The slope is the same for both equations but the y-intercept is different.<br \/>\nNo solutions<\/p>\n<p>Question 15.<br \/>\nDraw Conclusions The graph of a linear system appears in a textbook. You can see that the lines do not intersect on the graph, but also they do not appear to be parallel. Can you conclude that the system has no solution? Explain.<br \/>\n___________<\/p>\n<p>Answer:<\/p>\n<p>No; although the lines do not intersect on the graph, they intersect at a point that is not on the graph. To prove that a system has no solution, you must do so algebraically<\/p>\n<h3><a id=\"Solving_Solving_Special_Systems_Lesson_Check_\u2013_Page_No._264\"><\/a>Solving Solving Special Systems &#8211; Page No. 264<\/h3>\n<p>Question 16.<br \/>\nRepresent Real-World Problems Two school groups go to a roller skating rink. One group pays $243 for 36 admissions and 21 skate rentals. The other group pays $81 for 12 admissions and 7 skate rentals. Let x represent the cost of admission and let y represent the cost of a skate rental. Is there enough information to find values for x and y? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6636 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-22.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Lesson 5: Solving Solving Special Systems img 22\" width=\"179\" height=\"183\" \/><br \/>\n___________<\/p>\n<p>Answer:<br \/>\n36x + 21y = 243<br \/>\n12x + 7y = 81<br \/>\nwhere x is the cost of admission and y is the cost of stake rentals.<br \/>\nAlthough the information can be used to develop a system of linear equation, where each equation has two variables when the system is solved, the number of solutions is infinite, Mee the values of x and y cannot be determined.<br \/>\nNo<\/p>\n<p>Question 17.<br \/>\nRepresent Real-World Problems Juan and Tory are practicing for a track meet. They start their practice runs at the same point, but Tory starts 1 minute after Juan. Both run at a speed of 704 feet per minute. Does Tory catch up to Juan? Explain.<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nNo; Both Juan and Tory-run at the same rate, so the lines representing the distances each has run are parallel. There is no solution to the system<\/p>\n<p><strong>FOCUS ON HIGHER ORDER THINKING<\/strong><\/p>\n<p>Question 18.<br \/>\nJustify Reasoning A linear system with no solution consists of the equation y = 4x \u2212 3 and a second equation of the form y = mx + b. What can you say about the values of m and b? Explain your reasoning.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\ny = 4x &#8211; 3<br \/>\ny = mx + b<br \/>\nSince the system has no solutions, the two equations are parallel. The value of the slope, m would be the same i.e. 4. The value of y-intercept, b can be any number except -3 as b is different for parallel lines.<\/p>\n<p>Question 19.<br \/>\nJustify Reasoning A linear system with infinitely many solutions consists of the equation 3x + 5 = 8 and a second equation of the form Ax + By = C. What can you say about the values of A, B, and C? Explain your reasoning.<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\n3x + 5 = 8<br \/>\nAx + By = C<br \/>\nSince the system has infinitely many solutions, the values of A, B, and C must all be the same multiple of 3, 5, and 8, respectively. The two equations represent a single line, so the coefficients and constants of one equation must be a multiple of the other.<\/p>\n<p>Question 20.<br \/>\nDraw Conclusions Both the points (2, -2) and (4, -4) are solutions of a system of linear equations. What conclusions can you make about the equations and their graphs?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nIf a system has more than one solution, the equations represent the same line and have infinitely many solutions.<\/p>\n<h3><a id=\"Model_Quiz_\u2013_Page_No._265\"><\/a>Ready to Go On? &#8211; Model Quiz &#8211; Page No. 265<\/h3>\n<p><strong>8.1 Solving Systems of Linear Equations by Graphing<\/strong><\/p>\n<p><strong>Solve each system by graphing.<\/strong><\/p>\n<p>Question 1.<br \/>\n\\(\\left\\{\\begin{array}{l}y=x-1 \\\\y=2x-3\\end{array}\\right.\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6637 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-23.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Model Quiz img 23\" width=\"217\" height=\"217\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-23.jpg 217w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-23-150x150.jpg 150w\" sizes=\"(max-width: 217px) 100vw, 217px\" \/><br \/>\n(________ , ________)<\/p>\n<p>Answer:<br \/>\n(2, 1)<\/p>\n<p>Explanation:<br \/>\ny = x &#8211; 1<br \/>\ny = 2x &#8211; 3<br \/>\nGraph the equations on the same coordinate plane<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-3-1-300x185.png\" alt=\"grade 8 chapter 8 image 3\" width=\"300\" height=\"185\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-3-1-300x185.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-3-1.png 466w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe solution of the system is the point of intersection<br \/>\nThe solution is (2, 1)<\/p>\n<p>Question 2.<br \/>\n\\(\\left\\{\\begin{array}{l}x+2y=1 \\\\-x+y=2\\end{array}\\right.\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6638 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-24.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Model Quiz img 24\" width=\"214\" height=\"220\" \/><br \/>\n(________ , ________)<\/p>\n<p>Answer:<br \/>\n(-1, 1)<\/p>\n<p>Explanation:<br \/>\nx + 2y = 1<br \/>\n-x + y = 2<br \/>\nGraph the equations on same coordinate plane<br \/>\n<img loading=\"lazy\" class=\"alignnone size-medium wp-image-8076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-4-1-300x225.png\" alt=\"grade 8 chapter 8 image 4\" width=\"300\" height=\"225\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-4-1-300x225.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/08\/grade-8-chapter-8-image-4-1.png 437w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><br \/>\nThe solution of the system is the point of intersection<br \/>\nThe solution is (-1, 1)<\/p>\n<p><strong>8.2 Solving Systems by Substitution<\/strong><\/p>\n<p><strong>Solve each system of equations by substitution.<\/strong><\/p>\n<p>Question 3.<br \/>\n\\(\\left\\{\\begin{array}{l}y=2x \\\\x+y=-9\\end{array}\\right.\\)<br \/>\n(________ , ________)<\/p>\n<p>Answer:<br \/>\n(-3, -6)<\/p>\n<p>Explanation:<br \/>\ny = 2x<br \/>\nx + y = -9<br \/>\nSubstitute y from equation 1 in the other equation.<br \/>\nx + 2x = -9<br \/>\n3x = -9<br \/>\nx = -9\/3<br \/>\nx = -3<br \/>\nThen, y = 2(-3) = -6<br \/>\nThe Solution is (-3, -6)<\/p>\n<p>Question 4.<br \/>\n\\(\\left\\{\\begin{array}{l}3x-2y=11 \\\\x+2y=9\\end{array}\\right.\\)<br \/>\n(________ , ________)<\/p>\n<p>Answer:<br \/>\n(5, 2)<\/p>\n<p>Explanation:<br \/>\n3x &#8211; 2y = 11<br \/>\nx + 2y = 9<br \/>\nSolve for x in equation 2<br \/>\nx = &#8211; 2y + 9<br \/>\nSubstitute x from equation 2 in the other equation<br \/>\n3(-2y + 9) &#8211; 2y = 11<br \/>\n-6y + 27 -2y = 11<br \/>\n-8y = -16<br \/>\ny = -16\/-8 = 2<br \/>\nSubstitute y in any of the equations to find x<br \/>\nx + 2(2) = 9<br \/>\nx + 4 &#8211; 4 = 9 &#8211; 4<br \/>\nx = 5<br \/>\nThe solution is (5, 2)<\/p>\n<p><strong>8.3 Solving Systems by Elimination<\/strong><\/p>\n<p><strong>Solve each system of equations by adding or subtracting.<\/strong><\/p>\n<p>Question 5.<br \/>\n\\(\\left\\{\\begin{array}{l}3x+y=9 \\\\2x+y=5\\end{array}\\right.\\)<br \/>\n(________ , ________)<\/p>\n<p>Answer:<br \/>\n(4, -3)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}3x+y=9 \\\\2x+y=5\\end{array}\\right.\\)<br \/>\nSubtract the equations<br \/>\n3x + y = 9<br \/>\n-(2x + y = 5)<br \/>\ny is eliminated as it has reversed coefficients. Solve for x<br \/>\n3x + y &#8211; 2x &#8211; y = 9 &#8211; 5<br \/>\nx = 4<br \/>\nSubstituting x in either of the equation to find y<br \/>\n2(4) + y = 5<br \/>\n8 + y &#8211; 8 = 5 &#8211; 8<br \/>\ny = -3<br \/>\nThe solution is (4, -3)<\/p>\n<p>Question 6.<br \/>\n\\(\\left\\{\\begin{array}{l}-x-2y=4 \\\\3x+2y=4\\end{array}\\right.\\)<br \/>\n(________ , ________)<\/p>\n<p>Answer:<br \/>\n(4, -4)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}-x-2y=4 \\\\3x+2y=4\\end{array}\\right.\\)<br \/>\nAdd the equations<br \/>\n-x &#8211; 2y = 4<br \/>\n+(3x + 2y = 4)<br \/>\ny is eliminated as it has reversed coefficients. Solve for x<br \/>\n-x &#8211; 2y + 3x + 2y = 4 + 4<br \/>\n2x = 8<br \/>\nx = 8\/2 = 4<br \/>\nSubstituting x in either of the equation to find y<br \/>\n3(4) + 2y = 4<br \/>\n12 + 2y &#8211; 12 = 4 &#8211; 12<br \/>\n2y = -8<br \/>\ny = -8\/2 = -4<br \/>\nThe solution is (4, -4)<\/p>\n<p><strong>8.4 Solving Systems by Elimination with Multiplication<\/strong><\/p>\n<p><strong>Solve each system of equations by multiplying first.<\/strong><\/p>\n<p>Question 7.<br \/>\n\\(\\left\\{\\begin{array}{l}x+3y=-2 \\\\3x+4y=-1\\end{array}\\right.\\)<br \/>\n(________ , ________)<\/p>\n<p>Answer:<br \/>\n(1, -1)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}x+3y=-2 \\\\3x+4y=-1\\end{array}\\right.\\)<br \/>\nSubtract the equations<br \/>\n3x + 9y = -6<br \/>\n-(3x + 4y = -1)<br \/>\nx is eliminated as it has reversed coefficients. Solve for y<br \/>\n3x + 9y &#8211; 3x &#8211; 4y = -6 + 1<br \/>\n5y = -5<br \/>\ny = -5\/5<br \/>\ny = -1<br \/>\nSubstituting y in either of the equation to find x<br \/>\nx + 3(-1) = -2<br \/>\nx &#8211; 3 = -2<br \/>\nx = -2 + 3<br \/>\nx = 1<br \/>\nThe solution is (1, -1)<\/p>\n<p>Question 8.<br \/>\n\\(\\left\\{\\begin{array}{l}2x+8y=22 \\\\3x-2y=5\\end{array}\\right.\\)<br \/>\n(________ , ________)<\/p>\n<p>Answer:<br \/>\n(3, 2)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}2x+8y=22 \\\\3x-2y=5\\end{array}\\right.\\)<br \/>\nMultiply equation 2 by 4 so that y can be eliminated<br \/>\n4(3x &#8211; 2y = 5)<br \/>\n12x &#8211; 8y = 20<br \/>\nAdd the equations<br \/>\n2x + 8y = 22<br \/>\n+(12x &#8211; 8y = 20)<br \/>\ny is eliminated as it has reversed coefficients. Solve for x<br \/>\n2x + 8y + 12x &#8211; 8y = 22 + 20<br \/>\n14x = 42<br \/>\nx = 42\/14<br \/>\nx = 3<br \/>\nSubstituting y in either of the equation to find x<br \/>\n2(3) + 8y = 22<br \/>\n6 + 8y = 22<br \/>\n8y = 22 &#8211; 6<br \/>\n8y = 16<br \/>\ny = 16\/8<br \/>\ny = 2<br \/>\nThe solution is (3, 2)<\/p>\n<p><strong>8.5 Solving Special Systems<\/strong><\/p>\n<p><strong>Solve each system. Tell how many solutions each system has.<\/strong><\/p>\n<p>Question 9.<br \/>\n\\(\\left\\{\\begin{array}{l}-2x+8y=5 \\\\x-4y=-3\\end{array}\\right.\\)<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nno solution<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}-2x+8y=5 \\\\x-4y=-3\\end{array}\\right.\\)<br \/>\nMultiply equation 2 by 2 so that y can be eliminated<br \/>\n2(x &#8211; 4y = -3)<br \/>\n2x &#8211; 8y = -6<br \/>\nAdd the equations<br \/>\n-2x + 8y = 5<br \/>\n+(2x &#8211; 8y = -6)<br \/>\nx and y is eliminated<br \/>\n-2x + 8y + 2x &#8211; 8y = 5 &#8211; 6<br \/>\n0 = -1<br \/>\nThe statement is false. Hence, the system has no solution.<\/p>\n<p>Question 10.<br \/>\n\\(\\left\\{\\begin{array}{l}6x+18y=-12 \\\\x+3y=-2\\end{array}\\right.\\)<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\ninfinitely many solutions<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}6x+18y=-12 \\\\x+3y=-2\\end{array}\\right.\\)<br \/>\nMultiply equation 2 by 6 so that x can be eliminated<br \/>\n6(x + 3y = -2)<br \/>\n6x + 18y = -12<br \/>\nSubtract the equations<br \/>\n6x + 18y = -12<br \/>\n-(6x + 18y = -12)<br \/>\nx and y is eliminated<br \/>\n6x + 18y -6x -18y = -12 + 12<br \/>\n0 = 0<br \/>\nThe statement is true. Hence, the system has infinitely many solutions.<\/p>\n<p><strong>ESSENTIAL QUESTION<\/strong><\/p>\n<p>Question 11.<br \/>\nWhat are the possible solutions to a system of linear equations, and what do they represent graphically?<br \/>\nType below:<br \/>\n___________<\/p>\n<p>Answer:<br \/>\nSystem of linear equations can have no solution, which is represented by parallel lines; one solution, which is represented by intersecting lines; and infinitely many solutions, which is represented by overlapping lines.<\/p>\n<h3><a id=\"Mixed_Review_\u2013_Page_No._266\"><\/a>Selected Response &#8211; Mixed Review &#8211; Page No. 266<\/h3>\n<p>Question 1.<br \/>\nThe graph of which equation is shown?<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6639 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-25.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Mixed Review img 25\" width=\"230\" height=\"221\" \/><br \/>\nOptions:<br \/>\nA. y = \u22122x + 2<br \/>\nB. y = \u2212x + 2<br \/>\nC. y = 2x + 2<br \/>\nD. y = 2x + 1<\/p>\n<p>Answer:<br \/>\nC. y = 2x + 2<\/p>\n<p>Explanation:<br \/>\nOption A and B are eliminated as the slope of the graph is 2.<br \/>\nOption D is eliminated as the y-intercept from the graph should be 2.<br \/>\nOption C is the equation of the graph<\/p>\n<p>Question 2.<br \/>\nWhich best describes the solutions to the system<br \/>\n\\(\\left\\{\\begin{array}{l}x+y=-4 \\\\-2x-2y=0\\end{array}\\right.\\)<br \/>\nOptions:<br \/>\nA. one solution<br \/>\nB. no solution<br \/>\nC. infinitely many<br \/>\nD. (0, 0)<\/p>\n<p>Answer:<br \/>\nB. no solution<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}x+y=-4 \\\\-2x-2y=0\\end{array}\\right.\\)<br \/>\nMultply equation 1 by 2 so that x can be eliminated<br \/>\n2(x + y = -4)<br \/>\n2x + 2y = -8<br \/>\nAdd the equations<br \/>\n2x + 2y = -8<br \/>\n-2x &#8211; 2y = 0<br \/>\nx and y is eliminated<br \/>\n2x + 2y &#8211; 2x -2y = -8 + 0<br \/>\n0 = -8<br \/>\nThe statement is false. Hence, the system has no solution.<\/p>\n<p>Question 3.<br \/>\nWhich of the following represents 0.000056023 written in scientific notation?<br \/>\nOptions:<br \/>\nA. 5.6023 \u00d7 10<sup>5<\/sup><br \/>\nB. 5.6023 \u00d7 10<sup>4<\/sup><br \/>\nC. 5.6023 \u00d7 10<sup>-4<\/sup><br \/>\nD. 5.6023 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Answer:<br \/>\nD. 5.6023 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Explanation:<br \/>\nMove the decimal 5 points right to get the equation.<br \/>\nD. 5.6023 \u00d7 10<sup>-5<\/sup><\/p>\n<p>Question 4.<br \/>\nWhich is the solution to<br \/>\n\\(\\left\\{\\begin{array}{l}2x-y=1 \\\\4x+y=11\\end{array}\\right.\\)<br \/>\nOptions:<br \/>\nA. (2, 3)<br \/>\nB. (3, 2)<br \/>\nC. (-2, 3)<br \/>\nD. (3, -2)<\/p>\n<p>Answer:<br \/>\nA. (2, 3)<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}2x-y=1 \\\\4x+y=11\\end{array}\\right.\\)<br \/>\nAdd the equations<br \/>\n2x &#8211; y = 1<br \/>\n4x + y = 11<br \/>\ny is eliminated as it has reversed coefficients. Solve for x.<br \/>\n2x &#8211; y + 4x + y = 1 + 11<br \/>\n6x = 12<br \/>\nx = 12\/6 = 2<br \/>\nSubstituting x in either of the equation to find y<br \/>\n4(2) + y = 11<br \/>\n8 + y = 11<br \/>\ny = 11 &#8211; 8<br \/>\ny = 3<br \/>\nThe solution is (2, 3)<\/p>\n<p>Question 5.<br \/>\nWhich expression can you substitute in the indicated equation to solve<br \/>\n\\(\\left\\{\\begin{array}{l}3x-y=5 \\\\x+2y=4\\end{array}\\right.\\)<br \/>\nOptions:<br \/>\nA. 2y &#8211; 4 for x in 3x &#8211; y = 5<br \/>\nB. 4 &#8211; x for y in 3x &#8211; y = 5<br \/>\nC. 3x &#8211; 5 for y in 3x &#8211; y = 5<br \/>\nD. 3x &#8211; 5 for y in x + 2y = 4<\/p>\n<p>Answer:<br \/>\nD. 3x &#8211; 5 for y in x + 2y = 4<\/p>\n<p>Explanation:<br \/>\n\\(\\left\\{\\begin{array}{l}3x-y=5 \\\\x+2y=4\\end{array}\\right.\\)<br \/>\nSolve for y in equation 1<br \/>\ny = 3x &#8211; 5<br \/>\nSubstitute in other equation x + 2y = 4<\/p>\n<p>Question 6.<br \/>\nWhat is the solution to the system of linear equations shown on the graph?<br \/>\n<img loading=\"lazy\" class=\"alignnone wp-image-6640 size-full\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2020\/08\/Go-Math-Grade-8-Answer-Key-Chapter-8-Solving-Systems-of-Linear-Equations-img-26.jpg\" alt=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations Mixed Review img 26\" width=\"228\" height=\"159\" \/><br \/>\nOptions:<br \/>\nA. -1<br \/>\nB. -2<br \/>\nC. (-1, -2)<br \/>\nD. (-2, -1)<\/p>\n<p>Answer:<br \/>\nC. (-1, -2)<\/p>\n<p>Explanation:<br \/>\nThe point of intersection is (-1, -2), which is the solution of the system<\/p>\n<p>Question 7.<br \/>\nWhich step could you use to start solving<br \/>\n\\(\\left\\{\\begin{array}{l}x-6y=8 \\\\2x-5y=3\\end{array}\\right.\\)<br \/>\nOptions:<br \/>\nA. Add 2x &#8211; 5y = 3 to x &#8211; 6y = 8.<br \/>\nB. Multiply x &#8211; 6y = 8 by 2 and add it to 2x &#8211; 5y = 3.<br \/>\nC. Multiply x &#8211; 6y = 8 by 2 and subtract it from 2x &#8211; 5y = 3.<br \/>\nD. Substitute x = 6y &#8211; 8 for x in 2x &#8211; 5y = 3.<\/p>\n<p>Answer:<br \/>\nC. Multiply x &#8211; 6y = 8 by 2 and subtract it from 2x &#8211; 5y = 3.<\/p>\n<p>Explanation:<br \/>\nx &#8211; 6y = 8<br \/>\n2x &#8211; 5y = 3<br \/>\nMultiply the 1st equation by 2 so that the coefficient of variable x is the same in both equations<br \/>\nSubtract the equations as x has the same sign.<\/p>\n<p><strong>Mini-Task<\/strong><\/p>\n<p>Question 8.<br \/>\nA hot-air balloon begins rising from the ground at 4 meters per second at the same time a parachutist\u2019s chute opens at a height of 200 meters. The parachutist descends at 6 meters per second.<br \/>\na. Define the variables and write a system that represents the situation.<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\ny represents the distance from the ground and x represents the time in seconds<br \/>\ny = 4x<br \/>\ny = -6x + 200<\/p>\n<p>Question 8.<br \/>\nb. Find the solution. What does it mean?<br \/>\nType below:<br \/>\n_____________<\/p>\n<p>Answer:<br \/>\nSubstitute y from the equation 1 in the equation 2<br \/>\n4x = -6x + 200<br \/>\n4x + 6x = -6x + 200 + 6x<br \/>\n10x = 200<br \/>\nx = 200\/10 = 20<br \/>\nSubstitute x in any one of the equations and solve for x<br \/>\ny = 4(20) = 80<br \/>\nThe solution is (20, 80)<br \/>\nThe ballon and parachute meets after 20sec at 80m from the ground.<\/p>\n<h3>Final Words:<\/h3>\n<p>No Need to go to the tuitions or study hours if you follow our Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations PDF. I think the information seen in the Go Math 8th Grade Chapter 8 Solving Systems of Linear Equations is helpful for all the students. Get the step by step explanation for all the questions along with answers from the ccssmathanswers.com site. Bookmark our website to get the solutions for all the chapters in pdf format. All the Best Guys!!!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Students of Grade 8 can get a detailed explanation for all the questions in Go Math Answer Key Chapter 8 Solving Systems of Linear Equations. In addition to the exercise problems we also provide the solutions for the review test. So, go through all the answers and explanations provided by the math experts in Go &#8230; <a title=\"Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/go-math-grade-8-answer-key-chapter-8-solving-systems-of-linear-equations\/\" aria-label=\"More on Go Math Grade 8 Answer Key Chapter 8 Solving Systems of Linear Equations\">Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":8781,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2020\/12\/go-math-grade-8-chapter-8-solving-systems-of-linear-equations-answer-key.jpeg","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6613"}],"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\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=6613"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6613\/revisions"}],"predecessor-version":[{"id":92797,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/6613\/revisions\/92797"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/8781"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=6613"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=6613"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=6613"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}