{"id":155684,"date":"2022-03-26T00:55:11","date_gmt":"2022-03-25T19:25:11","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/linear-equations-in-two-variables-definition-explanation-formula-and-solved-examples\/"},"modified":"2023-01-02T12:47:58","modified_gmt":"2023-01-02T07:17:58","slug":"linear-equations-in-two-variables-definition-explanation-formula-and-solved-examples","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations-in-two-variables\/","title":{"rendered":"Linear Equations in Two Variables \u2013 Definition, Explanation, Formula and Solved Examples"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations-in-two-variables\/#The_Definition\" title=\"The Definition\">The Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations-in-two-variables\/#Pairs_of_Linear_Equations_in_Two_Variables\" title=\"Pairs of Linear Equations in Two Variables\">Pairs of Linear Equations in Two Variables<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations-in-two-variables\/#Linear_Equation_in_Two_Variables_Definition\" title=\"Linear Equation in Two Variables Definition\">Linear Equation in Two Variables Definition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations-in-two-variables\/#Linear_Equations_in_Variables\" title=\"Linear Equations in Variables\">Linear Equations in Variables<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations-in-two-variables\/#Linear_Equation_in_Two_Variable_Formula\" title=\"Linear Equation in Two Variable Formula\">Linear Equation in Two Variable Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations-in-two-variables\/#Solving_Linear_Equations_in_Two_Variables\" title=\"Solving Linear Equations in Two Variables\">Solving Linear Equations in Two Variables<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations-in-two-variables\/#Plotting_Graph_of_Linear_Equations_in_Two_Variables\" title=\"Plotting Graph of Linear Equations in Two Variables\">Plotting Graph of Linear Equations in Two Variables<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations-in-two-variables\/#Do_You_Know\" title=\"Do You Know\">Do You Know<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations-in-two-variables\/#Problems_and_Solutions\" title=\"Problems and Solutions\">Problems and Solutions<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"The_Definition\"><\/span>The Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>of a Virtual Machine<\/p>\n<p>A virtual machine is a software program that enables a computer to behave as if it were another separate computer. It allows a single physical computer to run multiple separate operating systems and applications concurrently.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-155683 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/linear-equations-in-two-variables-definition-explanation-formula-and-solved-examples.jpg\" alt=\"\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/linear-equations-in-two-variables-definition-explanation-formula-and-solved-examples.jpg?v=1648236307 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/linear-equations-in-two-variables-definition-explanation-formula-and-solved-examples-300x212.jpg?v=1648236307 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Pairs_of_Linear_Equations_in_Two_Variables\"><\/span>Pairs of Linear Equations in Two Variables<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A pair of linear equations in two variables is a set of two equations in two variables that are consistent, which means that they have the same solutions. The equations are written in standard form, which is Ax + By = C.<\/p>\n<p>To solve a pair of linear equations in two variables, you can use the following steps:<\/p>\n<p>1. Solve one of the equations for one of the variables.<\/p>\n<p>2. Substitute the value of the variable from the first equation into the other equation.<\/p>\n<p>3. Solve the equation for the variable.<\/p>\n<p>4. Check your solution.<\/p>\n<p>Here is an example of how to solve a pair of linear equations in two variables:<\/p>\n<p>x + 2y = 3<\/p>\n<p>3x &#8211; 2y = 5<\/p>\n<p>Solve the first equation for x.<\/p>\n<p>x = 3 &#8211; 2y<\/p>\n<p>Substitute 3 &#8211; 2y for x in the second equation.<\/p>\n<p>3x &#8211; 2y = 5<\/p>\n<p>3x &#8211; 2(3 &#8211; 2y) = 5<\/p>\n<p>3x &#8211; 6y = 5<\/p>\n<p>Solve the equation for y.<\/p>\n<p>y = 5 &#8211; 3x<\/p>\n<p>Check your solution.<\/p>\n<p>x + 2y = 3<\/p>\n<p>3x &#8211; 2y = 5<\/p>\n<p>3x &#8211; 2(5 &#8211; 3x) = 5<\/p>\n<p>3x &#8211; 2x = 5<\/p>\n<p>The solutions to the pair of linear equations are<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Linear_Equation_in_Two_Variables_Definition\"><\/span>Linear Equation in Two Variables Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A linear equation in two variables is an equation of the form<\/p>\n<p>ax + by = c<\/p>\n<p>where a, b, and c are real numbers. The equation represents a line in the plane with slope a and y-intercept b.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Linear_Equations_in_Variables\"><\/span>Linear Equations in Variables<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Ax + By = C<\/p>\n<p>A straight line can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Linear_Equation_in_Two_Variable_Formula\"><\/span>Linear Equation in Two Variable Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A linear equation in two variable is a mathematical equation in which each variable is represented by a single letter and the equation consists of a linear combination of these variables with a constant term.<\/p>\n<p>The general form of a linear equation in two variable is:<\/p>\n<p>ax + by = c<\/p>\n<p>Where a, b and c are constants.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Solving_Linear_Equations_in_Two_Variables\"><\/span>Solving Linear Equations in Two Variables<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A linear equation in two variables is an equation of the form<\/p>\n<p>ax + by = c<\/p>\n<p>where a, b, and c are real numbers and x and y are variables.<\/p>\n<p>There are three methods for solving linear equations in two variables:<\/p>\n<p>1. Substitution<br \/>\n2. Elimination<br \/>\n3. Graphical methods<\/p>\n<p>The following examples will illustrate how to solve linear equations in two variables using each of these methods.<\/p>\n<p>Example 1: Solve the equation 3x + 2y = 10 for y.<\/p>\n<p>Solution:<\/p>\n<p>1. Substitution: y = 10 \u2013 3x<\/p>\n<p>2. Elimination: Add 3x to both sides of the equation:<\/p>\n<p>3x + 2y = 10<\/p>\n<p>3x + 3x + 2y = 10<\/p>\n<p>2y = 10<\/p>\n<p>y = 5<\/p>\n<p>3. Graphical methods<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Plotting_Graph_of_Linear_Equations_in_Two_Variables\"><\/span>Plotting Graph of Linear Equations in Two Variables<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The graph of a linear equation in two variables is a line. The equation of the line can be written in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. The slope of the line is the change in y divided by the change in x. The y-intercept is the point at which the line intersects the y-axis.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Do_You_Know\"><\/span>Do You Know<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>What You&#8217;re Worth?<\/p>\n<p>Find out with the PayScale Salary Calculator.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Problems_and_Solutions\"><\/span>Problems and Solutions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Problem<\/p>\n<p>How can I keep my computer from going to sleep?<\/p>\n<p>Solution<\/p>\n<p>There are a few ways to keep your computer from going to sleep. One is to change the settings in the Power Options section of the Control Panel. Another is to use a program like caffeine to keep your computer from going to sleep.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Definition of a Virtual Machine A virtual machine is a software program that enables a computer to behave as [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Linear Equations in Two Variables","_yoast_wpseo_title":"Linear Equations in Two Variables \u2013 Definition, Explanation, Formula.","_yoast_wpseo_metadesc":"Learn about linear equations in two variables topic of maths in details explained by subject experts on infinitylearn.com","custom_permalink":"maths\/linear-equations-in-two-variables\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Linear Equations in 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