{"id":153702,"date":"2022-03-25T22:43:04","date_gmt":"2022-03-25T17:13:04","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/pair-of-linear-equation-in-two-variables\/"},"modified":"2023-01-02T15:30:07","modified_gmt":"2023-01-02T10:00:07","slug":"pair-of-linear-equation-in-two-variables","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/pair-of-linear-equation-in-two-variables\/","title":{"rendered":"Pair of Linear Equation in Two Variables"},"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\/pair-of-linear-equation-in-two-variables\/#Pair_of_Linear_Equation\" title=\"Pair of Linear Equation\">Pair of Linear Equation<\/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\/pair-of-linear-equation-in-two-variables\/#Pair_of_Linear_Equation_in_Two_variables_Introduction\" title=\"Pair of Linear Equation in Two variables Introduction\">Pair of Linear Equation in Two variables Introduction<\/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\/pair-of-linear-equation-in-two-variables\/#For_Example\" title=\"For Example\">For Example<\/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\/pair-of-linear-equation-in-two-variables\/#Expression_of_Pair_of_Linear_Equation_in_Two_Variables\" title=\"Expression of Pair of Linear Equation in Two Variables\">Expression of Pair of Linear Equation in Two 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\/pair-of-linear-equation-in-two-variables\/#Graphical_Expression_of_Pair_of_Linear_Equation_in_Two_Variables\" title=\"Graphical Expression of Pair of Linear Equation in Two Variables\">Graphical Expression of Pair of Linear Equation in Two Variables<\/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\/pair-of-linear-equation-in-two-variables\/#Algebraic_Method_of_Solving_a_Pair_of_Linear_Equations_of_Two_Variables\" title=\"Algebraic Method of Solving a Pair of Linear Equations of Two Variables.\">Algebraic Method of Solving a Pair of Linear Equations of 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\/pair-of-linear-equation-in-two-variables\/#What_is_a_Linear_equation\" title=\"What is a Linear equation?\">What is a Linear equation?<\/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\/pair-of-linear-equation-in-two-variables\/#How_to_Solve_the_Pair_of_Linear_Equations\" title=\"How to Solve the Pair of Linear Equations?\">How to Solve the Pair of Linear Equations?<\/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\/pair-of-linear-equation-in-two-variables\/#Representation\" title=\"Representation\">Representation<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Pair_of_Linear_Equation\"><\/span>Pair of Linear Equation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A linear equation is an equation in which each term is a constant multiple of the first term. Linear equations can be written in slope-intercept form, standard form, or point-slope form.<\/p>\n<p>A pair of linear equations is a set of two linear equations that are solved simultaneously. The equations are written in slope-intercept form and are graphed on the same coordinate plane. The point of intersection of the two graphs is the solution to the pair of equations.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-153701 size-medium\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/pair-of-linear-equation-in-two-variables-300x212.jpg\" alt=\"Pair of Linear Equation in Two Variables\" width=\"300\" height=\"212\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/pair-of-linear-equation-in-two-variables-300x212.jpg?v=1648228378 300w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/pair-of-linear-equation-in-two-variables.jpg?v=1648228378 606w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Pair_of_Linear_Equation_in_Two_variables_Introduction\"><\/span>Pair of Linear Equation in Two variables Introduction<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A linear equation in two variables is an equation that can be written in the form y = mx + b, where m and b are constants. This type of equation can be used to model a linear relationship between two variables.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"For_Example\"><\/span>For Example<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>In general, the use of a pronoun can refer back to a noun earlier in the text. For example, in the sentence &#8220;John is taller than any other student in the class,&#8221; the pronoun &#8220;he&#8221; refers back to the noun &#8220;John.&#8221; Pronouns can also be used to avoid repetition of a noun. For example, in the sentence &#8220;John is taller than any other student in the class, and he is also the captain of the basketball team,&#8221; the pronoun &#8220;he&#8221; is used to avoid repeating the noun &#8220;John.&#8221;<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Expression_of_Pair_of_Linear_Equation_in_Two_Variables\"><\/span>Expression of Pair of Linear Equation in Two Variables<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>If a and b are two real numbers, then the equation<\/p>\n<p>a + b = 0<\/p>\n<p>represents a pair of linear equations in two variables.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Graphical_Expression_of_Pair_of_Linear_Equation_in_Two_Variables\"><\/span>Graphical Expression of Pair of Linear Equation in Two Variables<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The graphical expression of a pair of linear equations in two variables is a line graph.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Algebraic_Method_of_Solving_a_Pair_of_Linear_Equations_of_Two_Variables\"><\/span>Algebraic Method of Solving a Pair of Linear Equations of Two Variables.<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To solve a pair of linear equations in two variables using the algebraic method, we 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 second equation.<\/p>\n<p>3. Solve the equation for the other variable.<\/p>\n<p>4. Check the solutions to make sure they work in both equations.<\/p>\n<p>Let&#8217;s solve the following pair of linear equations in two variables:<\/p>\n<p>2x + 3y = 5<\/p>\n<p>2x &#8211; 3y = -4<\/p>\n<p>Step 1: Solve one of the equations for one of the variables. We will solve the equation 2x + 3y = 5 for y.<\/p>\n<p>y = 5 &#8211; 2x<\/p>\n<p>Step 2: Substitute the value of y from the first equation into the second equation.<\/p>\n<p>2x &#8211; 3(5 &#8211; 2x) = -4<\/p>\n<p>2x &#8211; 15 + 3x = -4<\/p>\n<p>-13x = -19<\/p>\n<p>x = 1.46<\/p>\n<p>Step 3: Solve the equation for the other variable. We will solve the equation 2x &#8211; 3y = -4 for x.<\/p>\n<p>x = -4 + 3y<\/p>\n<p>Step 4: Check the solutions to make sure they work in both equations.<\/p>\n<p>2x + 3y = 5<\/p>\n<p>2x &#8211; 3y = -4<\/p>\n<h2><span class=\"ez-toc-section\" id=\"What_is_a_Linear_equation\"><\/span>What is a Linear equation?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A linear equation is an equation in which each term is linear.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_Solve_the_Pair_of_Linear_Equations\"><\/span>How to Solve the Pair of Linear Equations?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>There are a few steps in solving a pair of linear equations. The first step is to clear the fractions and decimals from the equations. Next, combine like terms on each side of the equation. Lastly, solve for the unknown variable.<\/p>\n<p>For this problem, the equations are:<\/p>\n<p>x + 2y = 3<br \/>\n4x &#8211; 5y = -11<\/p>\n<p>To clear the fractions and decimals, divide each side of the equation by the coefficient of the variable.<\/p>\n<p>x + 2y = 3<br \/>\n4x &#8211; 5y = -11<\/p>\n<p>x + 2y = 3<br \/>\n4x &#8211; 5y = -11<\/p>\n<p>x + 2y = 3<br \/>\n4x &#8211; 5y = -11<\/p>\n<p>Next, combine like terms on each side of the equation.<\/p>\n<p>x + 2y = 3<br \/>\n4x &#8211; 5y = -11<\/p>\n<p>x + 2y = 3<br \/>\n9x = -8<\/p>\n<p>Lastly, solve for the unknown variable.<\/p>\n<p>x = -8\/9<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Representation\"><\/span>Representation<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Representative democracy is a form of government in which people elect representatives to make decisions on their behalf. The representatives are elected by the people they represent.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pair of Linear Equation A linear equation is an equation in which each term is a constant multiple of the [&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":"Pair of Linear Equation in Two Variables","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Learn about Pair of Linear Equation in Two Variables topic of Maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/pair-of-linear-equation-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>Pair of Linear Equation in Two Variables - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Learn about Pair of Linear Equation in Two Variables topic of Maths in details explained by subject experts on infinitylearn.com.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/pair-of-linear-equation-in-two-variables\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Pair of Linear Equation in Two Variables - 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