{"id":10673,"date":"2017-06-05T14:58:08","date_gmt":"2017-06-05T14:58:08","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/prealgebra\/?post_type=chapter&#038;p=10673"},"modified":"2017-09-24T06:25:43","modified_gmt":"2017-09-24T06:25:43","slug":"verifying-solutions-to-equations-in-two-variables","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/wm-prealgebra\/chapter\/verifying-solutions-to-equations-in-two-variables\/","title":{"raw":"Verifying Solutions to Equations in Two Variables","rendered":"Verifying Solutions to Equations in Two Variables"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Given a coordinate pair, determine whether it is a solution to a two variable equation<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p data-type=\"title\">All the equations we solved so far have been equations with one variable. In almost every case, when we solved the equation we got exactly one solution. The process of solving an equation ended with a statement such as [latex]x=4[\/latex]. Then we checked the solution by substituting back into the equation.<\/p>\r\n<p data-type=\"title\">Here\u2019s an example of a linear equation in one variable, and its one solution.<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}3x+5=17\\hfill \\\\ \\\\ 3x=12\\hfill \\\\ x=4\\hfill \\end{array}[\/latex]<\/p>\r\nBut equations can have more than one variable. Equations with two variables can be written in the general form [latex]Ax+By=C[\/latex]. An equation of this form is called a linear equation in two variables.\r\n<div class=\"textbox shaded\">\r\n<h3>Linear Equation<\/h3>\r\nAn equation of the form [latex]Ax+By=C[\/latex], where [latex]A\\text{ and }B[\/latex] are not both zero, is called a linear equation in two variables.\r\n\r\n<\/div>\r\nNotice that the word \"line\" is in linear.\r\n\r\nHere is an example of a linear equation in two variables, [latex]x[\/latex] and [latex]y\\text{:}[\/latex]\r\n<p style=\"text-align: center;\">[latex]\\color{red}{A}x+\\color{blue}{B}y=\\color{green}{C}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]x+\\color{blue}{4}y=\\color{green}{8}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\color{red}{A=1},\\color{blue}{B=4},\\color{green}{C=8}[\/latex]<\/p>\r\nIs [latex]y=-5x+1[\/latex] a linear equation? It does not appear to be in the form [latex]Ax+By=C[\/latex]. But we could rewrite it in this form.\r\n<table id=\"eip-id1168468301870\" class=\"unnumbered unstyled\" summary=\" This image has two columns. The first column on the right is the equation y equals negative 5 times x plus 1. The second line in the left column reads, \" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>[latex]y=-5x+1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Add [latex]5x[\/latex] to both sides.<\/td>\r\n<td>[latex]y+5x=-5x+1+5x[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Simplify.<\/td>\r\n<td>[latex]y+5x=1[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Use the Commutative Property to put it in [latex]Ax+By=C[\/latex].<\/td>\r\n<td>[latex]\\color{red}{A}x+\\color{blue}{B}y=C[\/latex]\r\n\r\n[latex]5x+y=1[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nBy rewriting [latex]y=-5x+1[\/latex] as [latex]5x+y=1[\/latex], we can see that it is a linear equation in two variables because it can be written in the form [latex]Ax+By=C[\/latex].\r\n\r\nLinear equations in two variables have infinitely many solutions. For every number that is substituted for [latex]x[\/latex], there is a corresponding [latex]y[\/latex] value. This pair of values is a solution to the linear equation and is represented by the ordered pair [latex]\\left(x,y\\right)[\/latex]. When we substitute these values of [latex]x[\/latex] and [latex]y[\/latex] into the equation, the result is a true statement because the value on the left side is equal to the value on the right side.\r\n<div class=\"textbox shaded\">\r\n<h3>Solution to a Linear Equation in Two Variables<\/h3>\r\nAn ordered pair [latex]\\left(x,y\\right)[\/latex] is a solution to the linear equation [latex]Ax+By=C[\/latex], if the equation is a true statement when the [latex]x\\text{-}[\/latex] and [latex]y\\text{-values}[\/latex] of the ordered pair are substituted into the equation.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nDetermine which ordered pairs are solutions of the equation [latex]x+4y=8\\text{:}[\/latex]\r\n\r\n1. [latex]\\left(0,2\\right)[\/latex]\r\n2. [latex]\\left(2,-4\\right)[\/latex]\r\n3. [latex]\\left(-4,3\\right)[\/latex]\r\n\r\nSolution\r\nSubstitute the [latex]x\\text{- and}y\\text{-values}[\/latex] from each ordered pair into the equation and determine if the result is a true statement.\r\n<table id=\"eip-id1168469838906\" class=\"unnumbered unstyled\" summary=\"This image shows three columns. The first column is labeled \" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>1. [latex]\\left(0,2\\right)[\/latex]<\/td>\r\n<td>2. [latex]\\left(2,-4\\right)[\/latex]<\/td>\r\n<td>3. [latex]\\left(-4,3\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]x=\\color{blue}{0}, y=\\color{red}{2}[\/latex]\r\n\r\n[latex]x+4y=8[\/latex]\r\n\r\n[latex]\\color{blue}{0}+4\\cdot\\color{red}{2}\\stackrel{?}{=}8[\/latex]\r\n\r\n[latex]0+8\\stackrel{?}{=}8[\/latex]\r\n\r\n[latex]8=8\\checkmark[\/latex]<\/td>\r\n<td>[latex]x=\\color{blue}{2}, y=\\color{red}{-4}[\/latex]\r\n\r\n[latex]x+4y=8[\/latex]\r\n\r\n[latex]\\color{blue}{2}+4(\\color{red}{-4})\\stackrel{?}{=}8[\/latex]\r\n\r\n[latex]2+(-16)\\stackrel{?}{=}8[\/latex]\r\n\r\n[latex]-14\\not=8[\/latex]<\/td>\r\n<td>[latex]x=\\color{blue}{-4}, y=\\color{red}{3}[\/latex]\r\n\r\n[latex]x+4y=8[\/latex]\r\n\r\n[latex]\\color{blue}{-4}+4\\cdot\\color{red}{3}\\stackrel{?}{=}8[\/latex]\r\n\r\n[latex]-4+12\\stackrel{?}{=}8[\/latex]\r\n\r\n[latex]8=8\\checkmark[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\left(0,2\\right)[\/latex] is a solution.<\/td>\r\n<td>[latex]\\left(2,-4\\right)[\/latex] is not a solution.<\/td>\r\n<td>[latex]\\left(-4,3\\right)[\/latex] is a solution.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146928[\/ohm_question]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox exercises\">\r\n<h3>example<\/h3>\r\nDetermine which ordered pairs are solutions of the equation. [latex]y=5x - 1\\text{:}[\/latex]\r\n\r\n1. [latex]\\left(0,-1\\right)[\/latex]\r\n2. [latex]\\left(1,4\\right)[\/latex]\r\n3. [latex]\\left(-2,-7\\right)[\/latex]\r\n[reveal-answer q=\"941200\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"941200\"]\r\n\r\nSolution\r\nSubstitute the [latex]x\\text{-}[\/latex] and [latex]y\\text{-values}[\/latex] from each ordered pair into the equation and determine if it results in a true statement.\r\n<table id=\"eip-id1168466112848\" class=\"unnumbered unstyled\" summary=\"The figure shows three algebraic substitutions in three columns, a, b, and c. The equation is y equals 5 times x minus 1. The first substitution is for ordered pair (0, -1). The first line in column a reads x = 0, with 0 shown in blue and y = -1, with -1 shown in red. The next line is y = 5 x - 1. The next line is -1, shown in red = 5 open parentheses 0, shown in blue, closed parentheses - 1, with a question mark shown over the equal sign. The next line is -1 = 0 - 1, with a question mark over the equal sign. The next line is - 1 = -1, followed by a check mark. The last line is \" data-label=\"\">\r\n<tbody>\r\n<tr>\r\n<td>1. [latex]\\left(0,-1\\right)[\/latex]<\/td>\r\n<td>2. [latex]\\left(1,4\\right)[\/latex]<\/td>\r\n<td>3. [latex]\\left(-2,-7\\right)[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]x=\\color{blue}{0}, y=\\color{red}{-1}[\/latex]\r\n\r\n[latex]y=5x-1[\/latex]\r\n\r\n[latex]\\color{red}{-1}\\stackrel{?}{=}5(\\color{blue}{0})-1[\/latex]\r\n\r\n[latex]-1\\stackrel{?}{=}0-1[\/latex]\r\n\r\n[latex]-1=-1\\checkmark[\/latex]<\/td>\r\n<td>[latex]x=\\color{blue}{1}, y=\\color{red}{4}[\/latex]\r\n\r\n[latex]y=5x-1[\/latex]\r\n\r\n[latex]\\color{red}{4}\\stackrel{?}{=}5(\\color{blue}{1})-1[\/latex]\r\n\r\n[latex]4\\stackrel{?}{=}5-1[\/latex]\r\n\r\n[latex]4=4\\checkmark[\/latex]<\/td>\r\n<td>[latex]x=\\color{blue}{-2}, y=\\color{red}{-7}[\/latex]\r\n\r\n[latex]y=5x-1[\/latex]\r\n\r\n[latex]\\color{red}{-7}\\stackrel{?}{=}5(\\color{blue}{-2})-1[\/latex]\r\n\r\n[latex]-7\\stackrel{?}{=}-10-1[\/latex]\r\n\r\n[latex]-7\\not=-11[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>[latex]\\left(0,-1\\right)[\/latex] is a solution.<\/td>\r\n<td>[latex]\\left(1,4\\right)[\/latex] is a solution.<\/td>\r\n<td>[latex]\\left(-2,-7\\right)[\/latex] is not a solution.<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>try it<\/h3>\r\n[ohm_question]146929[\/ohm_question]\r\n\r\n[ohm_question]146941[\/ohm_question]\r\n\r\n<\/div>\r\nIb the next video you will see more\u00a0examples of how to determine whether an ordered pair is a solution to a linear equation.\r\n\r\nhttps:\/\/youtu.be\/pJtxugdFjEk","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Given a coordinate pair, determine whether it is a solution to a two variable equation<\/li>\n<\/ul>\n<\/div>\n<p data-type=\"title\">All the equations we solved so far have been equations with one variable. In almost every case, when we solved the equation we got exactly one solution. The process of solving an equation ended with a statement such as [latex]x=4[\/latex]. Then we checked the solution by substituting back into the equation.<\/p>\n<p data-type=\"title\">Here\u2019s an example of a linear equation in one variable, and its one solution.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{c}3x+5=17\\hfill \\\\ \\\\ 3x=12\\hfill \\\\ x=4\\hfill \\end{array}[\/latex]<\/p>\n<p>But equations can have more than one variable. Equations with two variables can be written in the general form [latex]Ax+By=C[\/latex]. An equation of this form is called a linear equation in two variables.<\/p>\n<div class=\"textbox shaded\">\n<h3>Linear Equation<\/h3>\n<p>An equation of the form [latex]Ax+By=C[\/latex], where [latex]A\\text{ and }B[\/latex] are not both zero, is called a linear equation in two variables.<\/p>\n<\/div>\n<p>Notice that the word &#8220;line&#8221; is in linear.<\/p>\n<p>Here is an example of a linear equation in two variables, [latex]x[\/latex] and [latex]y\\text{:}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\color{red}{A}x+\\color{blue}{B}y=\\color{green}{C}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]x+\\color{blue}{4}y=\\color{green}{8}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\color{red}{A=1},\\color{blue}{B=4},\\color{green}{C=8}[\/latex]<\/p>\n<p>Is [latex]y=-5x+1[\/latex] a linear equation? It does not appear to be in the form [latex]Ax+By=C[\/latex]. But we could rewrite it in this form.<\/p>\n<table id=\"eip-id1168468301870\" class=\"unnumbered unstyled\" summary=\"This image has two columns. The first column on the right is the equation y equals negative 5 times x plus 1. The second line in the left column reads,\" data-label=\"\">\n<tbody>\n<tr>\n<td>[latex]y=-5x+1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Add [latex]5x[\/latex] to both sides.<\/td>\n<td>[latex]y+5x=-5x+1+5x[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Simplify.<\/td>\n<td>[latex]y+5x=1[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Use the Commutative Property to put it in [latex]Ax+By=C[\/latex].<\/td>\n<td>[latex]\\color{red}{A}x+\\color{blue}{B}y=C[\/latex]<\/p>\n<p>[latex]5x+y=1[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>By rewriting [latex]y=-5x+1[\/latex] as [latex]5x+y=1[\/latex], we can see that it is a linear equation in two variables because it can be written in the form [latex]Ax+By=C[\/latex].<\/p>\n<p>Linear equations in two variables have infinitely many solutions. For every number that is substituted for [latex]x[\/latex], there is a corresponding [latex]y[\/latex] value. This pair of values is a solution to the linear equation and is represented by the ordered pair [latex]\\left(x,y\\right)[\/latex]. When we substitute these values of [latex]x[\/latex] and [latex]y[\/latex] into the equation, the result is a true statement because the value on the left side is equal to the value on the right side.<\/p>\n<div class=\"textbox shaded\">\n<h3>Solution to a Linear Equation in Two Variables<\/h3>\n<p>An ordered pair [latex]\\left(x,y\\right)[\/latex] is a solution to the linear equation [latex]Ax+By=C[\/latex], if the equation is a true statement when the [latex]x\\text{-}[\/latex] and [latex]y\\text{-values}[\/latex] of the ordered pair are substituted into the equation.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Determine which ordered pairs are solutions of the equation [latex]x+4y=8\\text{:}[\/latex]<\/p>\n<p>1. [latex]\\left(0,2\\right)[\/latex]<br \/>\n2. [latex]\\left(2,-4\\right)[\/latex]<br \/>\n3. [latex]\\left(-4,3\\right)[\/latex]<\/p>\n<p>Solution<br \/>\nSubstitute the [latex]x\\text{- and}y\\text{-values}[\/latex] from each ordered pair into the equation and determine if the result is a true statement.<\/p>\n<table id=\"eip-id1168469838906\" class=\"unnumbered unstyled\" summary=\"This image shows three columns. The first column is labeled\" data-label=\"\">\n<tbody>\n<tr>\n<td>1. [latex]\\left(0,2\\right)[\/latex]<\/td>\n<td>2. [latex]\\left(2,-4\\right)[\/latex]<\/td>\n<td>3. [latex]\\left(-4,3\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]x=\\color{blue}{0}, y=\\color{red}{2}[\/latex]<\/p>\n<p>[latex]x+4y=8[\/latex]<\/p>\n<p>[latex]\\color{blue}{0}+4\\cdot\\color{red}{2}\\stackrel{?}{=}8[\/latex]<\/p>\n<p>[latex]0+8\\stackrel{?}{=}8[\/latex]<\/p>\n<p>[latex]8=8\\checkmark[\/latex]<\/td>\n<td>[latex]x=\\color{blue}{2}, y=\\color{red}{-4}[\/latex]<\/p>\n<p>[latex]x+4y=8[\/latex]<\/p>\n<p>[latex]\\color{blue}{2}+4(\\color{red}{-4})\\stackrel{?}{=}8[\/latex]<\/p>\n<p>[latex]2+(-16)\\stackrel{?}{=}8[\/latex]<\/p>\n<p>[latex]-14\\not=8[\/latex]<\/td>\n<td>[latex]x=\\color{blue}{-4}, y=\\color{red}{3}[\/latex]<\/p>\n<p>[latex]x+4y=8[\/latex]<\/p>\n<p>[latex]\\color{blue}{-4}+4\\cdot\\color{red}{3}\\stackrel{?}{=}8[\/latex]<\/p>\n<p>[latex]-4+12\\stackrel{?}{=}8[\/latex]<\/p>\n<p>[latex]8=8\\checkmark[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\left(0,2\\right)[\/latex] is a solution.<\/td>\n<td>[latex]\\left(2,-4\\right)[\/latex] is not a solution.<\/td>\n<td>[latex]\\left(-4,3\\right)[\/latex] is a solution.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146928\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146928&theme=oea&iframe_resize_id=ohm146928&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox exercises\">\n<h3>example<\/h3>\n<p>Determine which ordered pairs are solutions of the equation. [latex]y=5x - 1\\text{:}[\/latex]<\/p>\n<p>1. [latex]\\left(0,-1\\right)[\/latex]<br \/>\n2. [latex]\\left(1,4\\right)[\/latex]<br \/>\n3. [latex]\\left(-2,-7\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q941200\">Show Solution<\/span><\/p>\n<div id=\"q941200\" class=\"hidden-answer\" style=\"display: none\">\n<p>Solution<br \/>\nSubstitute the [latex]x\\text{-}[\/latex] and [latex]y\\text{-values}[\/latex] from each ordered pair into the equation and determine if it results in a true statement.<\/p>\n<table id=\"eip-id1168466112848\" class=\"unnumbered unstyled\" summary=\"The figure shows three algebraic substitutions in three columns, a, b, and c. The equation is y equals 5 times x minus 1. The first substitution is for ordered pair (0, -1). The first line in column a reads x = 0, with 0 shown in blue and y = -1, with -1 shown in red. The next line is y = 5 x - 1. The next line is -1, shown in red = 5 open parentheses 0, shown in blue, closed parentheses - 1, with a question mark shown over the equal sign. The next line is -1 = 0 - 1, with a question mark over the equal sign. The next line is - 1 = -1, followed by a check mark. The last line is\" data-label=\"\">\n<tbody>\n<tr>\n<td>1. [latex]\\left(0,-1\\right)[\/latex]<\/td>\n<td>2. [latex]\\left(1,4\\right)[\/latex]<\/td>\n<td>3. [latex]\\left(-2,-7\\right)[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]x=\\color{blue}{0}, y=\\color{red}{-1}[\/latex]<\/p>\n<p>[latex]y=5x-1[\/latex]<\/p>\n<p>[latex]\\color{red}{-1}\\stackrel{?}{=}5(\\color{blue}{0})-1[\/latex]<\/p>\n<p>[latex]-1\\stackrel{?}{=}0-1[\/latex]<\/p>\n<p>[latex]-1=-1\\checkmark[\/latex]<\/td>\n<td>[latex]x=\\color{blue}{1}, y=\\color{red}{4}[\/latex]<\/p>\n<p>[latex]y=5x-1[\/latex]<\/p>\n<p>[latex]\\color{red}{4}\\stackrel{?}{=}5(\\color{blue}{1})-1[\/latex]<\/p>\n<p>[latex]4\\stackrel{?}{=}5-1[\/latex]<\/p>\n<p>[latex]4=4\\checkmark[\/latex]<\/td>\n<td>[latex]x=\\color{blue}{-2}, y=\\color{red}{-7}[\/latex]<\/p>\n<p>[latex]y=5x-1[\/latex]<\/p>\n<p>[latex]\\color{red}{-7}\\stackrel{?}{=}5(\\color{blue}{-2})-1[\/latex]<\/p>\n<p>[latex]-7\\stackrel{?}{=}-10-1[\/latex]<\/p>\n<p>[latex]-7\\not=-11[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>[latex]\\left(0,-1\\right)[\/latex] is a solution.<\/td>\n<td>[latex]\\left(1,4\\right)[\/latex] is a solution.<\/td>\n<td>[latex]\\left(-2,-7\\right)[\/latex] is not a solution.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>try it<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm146929\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146929&theme=oea&iframe_resize_id=ohm146929&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<p><iframe loading=\"lazy\" id=\"ohm146941\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=146941&theme=oea&iframe_resize_id=ohm146941&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<p>Ib the next video you will see more\u00a0examples of how to determine whether an ordered pair is a solution to a linear equation.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Ex: Determine If An Ordered Pair is a Solution to a Linear Equation\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/pJtxugdFjEk?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-10673\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Original<\/div><ul class=\"citation-list\"><li>Question ID 146941, 146929, 146928, 146927. <strong>Authored by<\/strong>: Lumen Learning. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Ex: Determine If An Ordered Pair is a Solution to a Linear Equation. <strong>Authored by<\/strong>: James Sousa (mathispower4u.com). <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/pJtxugdFjEk\">https:\/\/youtu.be\/pJtxugdFjEk<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Specific attribution<\/div><ul class=\"citation-list\"><li>Prealgebra. <strong>Provided by<\/strong>: OpenStax. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":5,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"},{\"type\":\"original\",\"description\":\"Question ID 146941, 146929, 146928, 146927\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Ex: Determine If An Ordered Pair is a Solution to a Linear Equation\",\"author\":\"James Sousa 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