{"id":15358,"date":"2021-10-11T23:05:37","date_gmt":"2021-10-11T23:05:37","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/read-ordered-pairs-as-solutions-to-systems\/"},"modified":"2022-01-09T19:23:00","modified_gmt":"2022-01-09T19:23:00","slug":"read-ordered-pairs-as-solutions-to-systems","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/read-ordered-pairs-as-solutions-to-systems\/","title":{"raw":"Ordered Pairs as Solutions to Systems","rendered":"Ordered Pairs as Solutions to Systems"},"content":{"raw":"<div class=\"bcc-box bcc-highlight\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Evaluate ordered pairs as solutions to systems<\/li>\r\n<\/ul>\r\n<\/div>\r\nA <strong>system of linear equations<\/strong> consists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously. To find the unique solution to a system of linear equations, we must find a numerical value for each variable in the system that will satisfy all equations in the system at the same time.\u00a0In this section, we will look at systems of linear equations in two variables which consist of two equations that each contain two different variables.\r\n<h2 id=\"title2\">Determine whether an ordered pair is a solution for a system of linear equations<\/h2>\r\nConsider the following system of linear equations in two variables.\r\n<div style=\"text-align: center;\">[latex]\\begin{array}{l}2x+y=\\text{ }15\\\\3x-y=\\text{ }5\\end{array}[\/latex]<\/div>\r\nThe <em>solution<\/em> to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. In this example, the ordered pair\u00a0 [latex](4, 7)[\/latex] is the solution to the system of linear equations. We can verify the solution by substituting the values into each equation to see if the ordered pair satisfies both equations. Shortly, we will investigate methods of finding such a solution if it exists.\r\n<div style=\"text-align: center;\">[latex]\\begin{array}{l}2\\left(4\\right)+\\left(7\\right)=15\\text{ }\\text{True}\\hfill \\\\ 3\\left(4\\right)-\\left(7\\right)=5\\text{ }\\text{True}\\hfill \\end{array}[\/latex]<\/div>\r\n<div><\/div>\r\n<div class=\"textbox\">\r\n<h3>How To: Given a system of linear equations and an ordered pair, determine whether the ordered pair is a solution<\/h3>\r\n<ol>\r\n \t<li>Substitute the ordered pair into each equation in the system.<\/li>\r\n \t<li>Determine whether true statements result from the substitution in both equations; if so, the ordered pair is a solution.<\/li>\r\n<\/ol>\r\n<\/div>\r\n<img class=\"size-medium wp-image-388 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/02\/04064355\/image009-2-300x300.jpg\" alt=\"image009-2\" width=\"300\" height=\"300\" \/>\r\n\r\nThe lines in the graph above are defined as\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}2x-y=-4\\\\ x-y=-1\\end{array}[\/latex].<\/p>\r\nThey cross at what appears to be [latex]\\left(-3,-2\\right)[\/latex].\r\n\r\nUsing algebra, we can verify that this shared point is actually [latex]\\left(-3,-2\\right)[\/latex] and not [latex]\\left(-2.999,-1.999\\right)[\/latex]. By substituting the [latex]x[\/latex]- and [latex]y[\/latex]-values of the ordered pair into the equation of each line, you can test whether the point is on both lines. If the substitution results in a true statement, then you have found a\u00a0solution to the system of equations!\r\n\r\nSince the solution of the system must be a solution to all the equations in the system, you will need to check the point in each equation. In the following example, we will substitute [latex]-3[\/latex] for [latex]x[\/latex] and [latex]-2[\/latex] for [latex]y[\/latex] in each equation to test whether it is actually the solution.\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nIs [latex]\\left(-3,-2\\right)[\/latex] a solution of the system\r\n\r\n[latex]\\begin{array}{r}2x-y=-4\\\\ x-y=-1\\end{array}[\/latex]\r\n\r\n[reveal-answer q=\"919027\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"919027\"]Test\u00a0[latex]2x-y=-4[\/latex] first:\r\n\r\n[latex]\\begin{array}{r}2(-3)-(-2) = -4\\\\-6+2=-4\\\\-4 = -4\\\\\\text{TRUE}\\end{array}[\/latex]\r\n\r\nNow test [latex]x-y=-1[\/latex].\r\n\r\n[latex]\\begin{array}{r}(-3)-(-2) = -1\\\\-3+2=-1\\\\-1 = -1\\\\\\text{TRUE}\\end{array}[\/latex]\r\n\r\n[latex]\\left(-3,-2\\right)[\/latex] is a solution of [latex]x-y=-1[\/latex]\r\n\r\nSince[latex]\\left(-3,-2\\right)[\/latex] is a solution of each of the equations in the system,[latex]\\left(-3,-2\\right)[\/latex] is a solution of the system.\r\n<h4>Answer<\/h4>\r\n[latex]\\left(-3,-2\\right)[\/latex] is a solution to the system.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"bcc-box bcc-info\">\r\n<h3>Example<\/h3>\r\nIs [latex](3, 9)[\/latex] a solution of the system\r\n\r\n[latex]\\begin{array}{r}y=3x\\\\2x\u2013y=6\\end{array}[\/latex]\r\n\r\n[reveal-answer q=\"190963\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"190963\"]Since the solution of the system must be a solution to all the equations in the system, check the point in each equation.\r\n\r\nSubstitute [latex]3[\/latex] for [latex]x[\/latex] and [latex]9[\/latex] for [latex]y[\/latex] in each equation.\r\n\r\n[latex]\\begin{array}{l}y=3x\\\\9=3\\left(3\\right)\\\\\\text{TRUE}\\end{array}[\/latex]\r\n\r\n[latex](3, 9)[\/latex] is a solution of [latex]y=3x[\/latex].\r\n\r\n[latex]\\begin{array}{r}2x\u2013y=6\\\\2\\left(3\\right)\u20139=6\\\\6\u20139=6\\\\-3=6\\\\\\text{FALSE}\\end{array}[\/latex]\r\n\r\n[latex](3, 9)[\/latex] is not a solution of [latex]2x\u2013y=6[\/latex].\r\n\r\nSince [latex](3, 9)[\/latex] is not a solution of one of the equations in the system, it cannot be a solution of the system.\r\n<h4>Answer<\/h4>\r\n[latex](3, 9)[\/latex] is not a solution to the system.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Example<\/h3>\r\nDetermine whether the ordered pair [latex]\\left(5,1\\right)[\/latex] is a solution to the given system of equations.\r\n<div style=\"text-align: center;\">[latex]\\begin{array}{l}x+3y=8\\hfill \\\\ 2x - 9=y\\hfill \\end{array}[\/latex]<\/div>\r\n[reveal-answer q=\"322824\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"322824\"]\r\n\r\nSubstitute the ordered pair [latex]\\left(5,1\\right)[\/latex] into both equations.\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{ll}\\left(5\\right)+3\\left(1\\right)=8\\hfill &amp; \\hfill \\\\ \\text{ }8=8\\hfill &amp; \\text{True}\\hfill \\\\2\\left(5\\right)-9=\\left(1\\right)\\hfill &amp; \\hfill \\\\ \\text{ }\\text{1=1}\\hfill &amp; \\text{True}\\hfill \\end{array}[\/latex]<\/p>\r\nThe ordered pair [latex]\\left(5,1\\right)[\/latex] satisfies both equations, so it is the solution to the system.\r\n\r\nWe can see the solution clearly by plotting the graph of each equation. Since the solution is an ordered pair that satisfies both equations, it is a point on both of the lines and thus the point of intersection of the two lines.\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/07\/01222634\/CNX_Precalc_Figure_09_01_0032.jpg\" alt=\"A graph of two lines running through the point five, one. The first line's equation is x plus 3y equals 8. The second line's equation is 2x minus 9 equals y.\" width=\"487\" height=\"365\" \/>\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Think About It<\/h3>\r\nIs [latex](\u22122,4)[\/latex] a solution for the system\r\n\r\n[latex]\\begin{array}{r}y=2x\\\\3x+2y=1\\end{array}[\/latex]\r\n\r\nBefore you do any calculations, look at the point given and the first equation in the system. \u00a0Can you predict the answer to the question without doing any algebra?\r\n[reveal-answer q=\"598405\"]Show Solution[\/reveal-answer]\r\n[hidden-answer a=\"598405\"]\r\n\r\nSubstitute [latex]-2[\/latex] for [latex]x[\/latex], and [latex]4[\/latex] for [latex]y[\/latex] into the first equation:\r\n\r\n[latex]\\begin{array}{l}y=2x\\\\4=2\\left(-2\\right)\\\\4=-4\\\\\\text{FALSE}\\end{array}[\/latex]\r\n\r\nYou can stop testing because a point that is a solution to the system will be a solution to both equations in the system.\r\n\r\n[latex](\u22122,4)[\/latex] is NOT a solution for the system\r\n\r\n[latex]\\begin{array}{r}y=2x\\\\3x+2y=1\\end{array}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\nIn the following video, we will show another example of how to verify whether an ordered pair is a solution to a system of equations.\r\n\r\nhttps:\/\/youtu.be\/2IxgKgjX00k\r\n\r\nRemember that in order to be a solution to the system of equations, the values of the point must be a solution for both equations. Once you find one equation for which the point is false, you have determined that it is not a solution for the system.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Try It<\/h3>\r\n[ohm_question]48988[\/ohm_question]\r\n\r\n<\/div>\r\n<h2>Contribute!<\/h2>\r\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\r\n<a style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\" href=\"https:\/\/docs.google.com\/document\/d\/1i2cjdQwL7fkjxUpuGDm1dgKKcKxQmsjUNPuALmDzrkY\" target=\"_blank\" rel=\"noopener\">Improve this page<\/a><a style=\"margin-left: 16px;\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\" target=\"_blank\" rel=\"noopener\">Learn More<\/a>","rendered":"<div class=\"bcc-box bcc-highlight\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Evaluate ordered pairs as solutions to systems<\/li>\n<\/ul>\n<\/div>\n<p>A <strong>system of linear equations<\/strong> consists of two or more linear equations made up of two or more variables such that all equations in the system are considered simultaneously. To find the unique solution to a system of linear equations, we must find a numerical value for each variable in the system that will satisfy all equations in the system at the same time.\u00a0In this section, we will look at systems of linear equations in two variables which consist of two equations that each contain two different variables.<\/p>\n<h2 id=\"title2\">Determine whether an ordered pair is a solution for a system of linear equations<\/h2>\n<p>Consider the following system of linear equations in two variables.<\/p>\n<div style=\"text-align: center;\">[latex]\\begin{array}{l}2x+y=\\text{ }15\\\\3x-y=\\text{ }5\\end{array}[\/latex]<\/div>\n<p>The <em>solution<\/em> to a system of linear equations in two variables is any ordered pair that satisfies each equation independently. In this example, the ordered pair\u00a0 [latex](4, 7)[\/latex] is the solution to the system of linear equations. We can verify the solution by substituting the values into each equation to see if the ordered pair satisfies both equations. Shortly, we will investigate methods of finding such a solution if it exists.<\/p>\n<div style=\"text-align: center;\">[latex]\\begin{array}{l}2\\left(4\\right)+\\left(7\\right)=15\\text{ }\\text{True}\\hfill \\\\ 3\\left(4\\right)-\\left(7\\right)=5\\text{ }\\text{True}\\hfill \\end{array}[\/latex]<\/div>\n<div><\/div>\n<div class=\"textbox\">\n<h3>How To: Given a system of linear equations and an ordered pair, determine whether the ordered pair is a solution<\/h3>\n<ol>\n<li>Substitute the ordered pair into each equation in the system.<\/li>\n<li>Determine whether true statements result from the substitution in both equations; if so, the ordered pair is a solution.<\/li>\n<\/ol>\n<\/div>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-388 aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1468\/2016\/02\/04064355\/image009-2-300x300.jpg\" alt=\"image009-2\" width=\"300\" height=\"300\" \/><\/p>\n<p>The lines in the graph above are defined as<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{r}2x-y=-4\\\\ x-y=-1\\end{array}[\/latex].<\/p>\n<p>They cross at what appears to be [latex]\\left(-3,-2\\right)[\/latex].<\/p>\n<p>Using algebra, we can verify that this shared point is actually [latex]\\left(-3,-2\\right)[\/latex] and not [latex]\\left(-2.999,-1.999\\right)[\/latex]. By substituting the [latex]x[\/latex]&#8211; and [latex]y[\/latex]-values of the ordered pair into the equation of each line, you can test whether the point is on both lines. If the substitution results in a true statement, then you have found a\u00a0solution to the system of equations!<\/p>\n<p>Since the solution of the system must be a solution to all the equations in the system, you will need to check the point in each equation. In the following example, we will substitute [latex]-3[\/latex] for [latex]x[\/latex] and [latex]-2[\/latex] for [latex]y[\/latex] in each equation to test whether it is actually the solution.<\/p>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Is [latex]\\left(-3,-2\\right)[\/latex] a solution of the system<\/p>\n<p>[latex]\\begin{array}{r}2x-y=-4\\\\ x-y=-1\\end{array}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q919027\">Show Solution<\/span><\/p>\n<div id=\"q919027\" class=\"hidden-answer\" style=\"display: none\">Test\u00a0[latex]2x-y=-4[\/latex] first:<\/p>\n<p>[latex]\\begin{array}{r}2(-3)-(-2) = -4\\\\-6+2=-4\\\\-4 = -4\\\\\\text{TRUE}\\end{array}[\/latex]<\/p>\n<p>Now test [latex]x-y=-1[\/latex].<\/p>\n<p>[latex]\\begin{array}{r}(-3)-(-2) = -1\\\\-3+2=-1\\\\-1 = -1\\\\\\text{TRUE}\\end{array}[\/latex]<\/p>\n<p>[latex]\\left(-3,-2\\right)[\/latex] is a solution of [latex]x-y=-1[\/latex]<\/p>\n<p>Since[latex]\\left(-3,-2\\right)[\/latex] is a solution of each of the equations in the system,[latex]\\left(-3,-2\\right)[\/latex] is a solution of the system.<\/p>\n<h4>Answer<\/h4>\n<p>[latex]\\left(-3,-2\\right)[\/latex] is a solution to the system.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"bcc-box bcc-info\">\n<h3>Example<\/h3>\n<p>Is [latex](3, 9)[\/latex] a solution of the system<\/p>\n<p>[latex]\\begin{array}{r}y=3x\\\\2x\u2013y=6\\end{array}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q190963\">Show Solution<\/span><\/p>\n<div id=\"q190963\" class=\"hidden-answer\" style=\"display: none\">Since the solution of the system must be a solution to all the equations in the system, check the point in each equation.<\/p>\n<p>Substitute [latex]3[\/latex] for [latex]x[\/latex] and [latex]9[\/latex] for [latex]y[\/latex] in each equation.<\/p>\n<p>[latex]\\begin{array}{l}y=3x\\\\9=3\\left(3\\right)\\\\\\text{TRUE}\\end{array}[\/latex]<\/p>\n<p>[latex](3, 9)[\/latex] is a solution of [latex]y=3x[\/latex].<\/p>\n<p>[latex]\\begin{array}{r}2x\u2013y=6\\\\2\\left(3\\right)\u20139=6\\\\6\u20139=6\\\\-3=6\\\\\\text{FALSE}\\end{array}[\/latex]<\/p>\n<p>[latex](3, 9)[\/latex] is not a solution of [latex]2x\u2013y=6[\/latex].<\/p>\n<p>Since [latex](3, 9)[\/latex] is not a solution of one of the equations in the system, it cannot be a solution of the system.<\/p>\n<h4>Answer<\/h4>\n<p>[latex](3, 9)[\/latex] is not a solution to the system.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Example<\/h3>\n<p>Determine whether the ordered pair [latex]\\left(5,1\\right)[\/latex] is a solution to the given system of equations.<\/p>\n<div style=\"text-align: center;\">[latex]\\begin{array}{l}x+3y=8\\hfill \\\\ 2x - 9=y\\hfill \\end{array}[\/latex]<\/div>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q322824\">Show Solution<\/span><\/p>\n<div id=\"q322824\" class=\"hidden-answer\" style=\"display: none\">\n<p>Substitute the ordered pair [latex]\\left(5,1\\right)[\/latex] into both equations.<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{ll}\\left(5\\right)+3\\left(1\\right)=8\\hfill & \\hfill \\\\ \\text{ }8=8\\hfill & \\text{True}\\hfill \\\\2\\left(5\\right)-9=\\left(1\\right)\\hfill & \\hfill \\\\ \\text{ }\\text{1=1}\\hfill & \\text{True}\\hfill \\end{array}[\/latex]<\/p>\n<p>The ordered pair [latex]\\left(5,1\\right)[\/latex] satisfies both equations, so it is the solution to the system.<\/p>\n<p>We can see the solution clearly by plotting the graph of each equation. Since the solution is an ordered pair that satisfies both equations, it is a point on both of the lines and thus the point of intersection of the two lines.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/121\/2016\/07\/01222634\/CNX_Precalc_Figure_09_01_0032.jpg\" alt=\"A graph of two lines running through the point five, one. The first line's equation is x plus 3y equals 8. The second line's equation is 2x minus 9 equals y.\" width=\"487\" height=\"365\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Think About It<\/h3>\n<p>Is [latex](\u22122,4)[\/latex] a solution for the system<\/p>\n<p>[latex]\\begin{array}{r}y=2x\\\\3x+2y=1\\end{array}[\/latex]<\/p>\n<p>Before you do any calculations, look at the point given and the first equation in the system. \u00a0Can you predict the answer to the question without doing any algebra?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q598405\">Show Solution<\/span><\/p>\n<div id=\"q598405\" class=\"hidden-answer\" style=\"display: none\">\n<p>Substitute [latex]-2[\/latex] for [latex]x[\/latex], and [latex]4[\/latex] for [latex]y[\/latex] into the first equation:<\/p>\n<p>[latex]\\begin{array}{l}y=2x\\\\4=2\\left(-2\\right)\\\\4=-4\\\\\\text{FALSE}\\end{array}[\/latex]<\/p>\n<p>You can stop testing because a point that is a solution to the system will be a solution to both equations in the system.<\/p>\n<p>[latex](\u22122,4)[\/latex] is NOT a solution for the system<\/p>\n<p>[latex]\\begin{array}{r}y=2x\\\\3x+2y=1\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<p>In the following video, we will show another example of how to verify whether an ordered pair is a solution to a system of equations.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Determine if an Ordered Pair is a Solution to a System of Linear Equations\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/2IxgKgjX00k?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>Remember that in order to be a solution to the system of equations, the values of the point must be a solution for both equations. Once you find one equation for which the point is false, you have determined that it is not a solution for the system.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Try It<\/h3>\n<p><iframe loading=\"lazy\" id=\"ohm48988\" class=\"resizable\" src=\"https:\/\/ohm.lumenlearning.com\/multiembedq.php?id=48988&theme=oea&iframe_resize_id=ohm48988&show_question_numbers\" width=\"100%\" height=\"150\"><\/iframe><\/p>\n<\/div>\n<h2>Contribute!<\/h2>\n<div style=\"margin-bottom: 8px;\">Did you have an idea for improving this content? We\u2019d love your input.<\/div>\n<p><a style=\"font-size: 10pt; font-weight: 600; color: #077fab; text-decoration: none; border: 2px solid #077fab; border-radius: 7px; padding: 5px 25px; text-align: center; cursor: pointer; line-height: 1.5em;\" href=\"https:\/\/docs.google.com\/document\/d\/1i2cjdQwL7fkjxUpuGDm1dgKKcKxQmsjUNPuALmDzrkY\" target=\"_blank\" rel=\"noopener\">Improve this page<\/a><a style=\"margin-left: 16px;\" href=\"https:\/\/docs.google.com\/document\/d\/1vy-T6DtTF-BbMfpVEI7VP_R7w2A4anzYZLXR8Pk4Fu4\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/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-15358\">\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>Determine if an Ordered Pair is a Solution to a System of Linear Equations. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/2IxgKgjX00k\">https:\/\/youtu.be\/2IxgKgjX00k<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em><\/li><li>Revision and Adaptation. <strong>Provided 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><li>Determine if an Ordered Pair is a Solution to a System of Linear Inequalities. <strong>Authored by<\/strong>: James Sousa (Mathispower4u.com) for Lumen Learning. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/o9hTFJEBcXs\">https:\/\/youtu.be\/o9hTFJEBcXs<\/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, Shared previously<\/div><ul class=\"citation-list\"><li>Unit 14: Systems of Equations and Inequalities, from Developmental Math: An Open Program. <strong>Provided by<\/strong>: Monterey Institute of Technology and Education. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/\">http:\/\/nrocnetwork.org\/resources\/downloads\/nroc-math-open-textbook-units-1-12-pdf-and-word-formats\/<\/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>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":167848,"menu_order":3,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Determine if an Ordered Pair is a Solution to a System of Linear Equations\",\"author\":\"James Sousa (Mathispower4u.com) for Lumen Learning\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/2IxgKgjX00k\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"original\",\"description\":\"Revision and Adaptation\",\"author\":\"\",\"organization\":\"Lumen Learning\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Unit 14: Systems of Equations and Inequalities, from Developmental Math: An Open Program\",\"author\":\"\",\"organization\":\"Monterey Institute of Technology and Education\",\"url\":\" 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