{"id":153830,"date":"2022-03-25T22:51:35","date_gmt":"2022-03-25T17:21:35","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/solving-linear-equations\/"},"modified":"2024-08-29T19:01:06","modified_gmt":"2024-08-29T13:31:06","slug":"solving-linear-equations","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations\/","title":{"rendered":"Linear Equation"},"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\/#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-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations\/#Types_of_Linear_Equations\" title=\"Types of Linear Equations\">Types of Linear Equations<\/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\/#Linear_Equations_Examples\" title=\"Linear Equations Examples\">Linear Equations Examples<\/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\/#Linear_Equation_Forms\" title=\"Linear Equation Forms\">Linear Equation Forms<\/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\/#Methods_to_Solve_the_Linear_Equations\" title=\"Methods to Solve the Linear Equations\">Methods to Solve the Linear Equations<\/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\/#General_Steps_to_Solve_Linear_Equations\" title=\"General Steps to Solve Linear Equations\">General Steps to Solve Linear Equations<\/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\/#Tips_on_Linear_Equations\" title=\"Tips on Linear Equations\">Tips on Linear Equations<\/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\/#Solved_Examples_of_Linear_Equations\" title=\"Solved Examples of Linear Equations\">Solved Examples 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\/linear-equations\/#Practice_Questions_on_Linear_Equations\" title=\"Practice Questions on Linear Equations\">Practice Questions on Linear Equations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations\/#Linear_Equations_FAQs\" title=\"Linear Equations: FAQs\">Linear Equations: FAQs<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations\/#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-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations\/#How_do_you_solve_a_linear_equation_in_one_variable\" title=\"How do you solve a linear equation in one variable?\">How do you solve a linear equation in one variable?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/linear-equations\/#How_can_you_check_if_your_solution_to_a_linear_equation_is_correct\" title=\"How can you check if your solution to a linear equation is correct?\">How can you check if your solution to a linear equation is correct?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p>A linear equation is an equation where the highest power of the variable is one. Therefore, a Linear Equation is also known as a one-degree equation. Read this article to learn more about the Linear Equations.<\/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 algebraic expression with the highest degree of any variable equal to 1. This means that no variable is raised to a power greater than 1. One must note that when it is plotted on a graph, a linear equation always produces a straight line.<\/p>\n<p style=\"text-align: center;\"><strong>Also Check:<a href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/\"> Circumstance of Circle<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Types_of_Linear_Equations\"><\/span>Types of Linear Equations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Linear equations can involve one or two variables. Definitions and examples of these types are discussed below.<\/p>\n<p><b>Linear Equations in One Variable<\/b><\/p>\n<p>The linear equation formed with a single variable forms the first type of Linear Equation.  For an equation with one variable, the standard form is Ax + B = 0, where,<\/p>\n<p>x represents the variable.<\/p>\n<p>A is the coefficient of x.<\/p>\n<p>B is a constant.<\/p>\n<p>For example: x+2=5<\/p>\n<p><b>Linear Equations in Two Variables<\/b><\/p>\n<p>The linear equation formed with two variables form the second type of Linear Equation.  For an equation with two variables, the standard form of a linear equation is Ax + By = C , where,<\/p>\n<p>x and y are the variables.<\/p>\n<p>A and B are coefficients.<\/p>\n<p>C is a constant.<\/p>\n<p>For example: x+2y=15<\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/average\/\">Average<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Linear_Equations_Examples\"><\/span>Linear Equations Examples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>For a better understanding of one or two variables linear equations and non-linear equations, observe the table below.<\/p>\n<table>\n<tbody>\n<tr>\n<td>Equations<\/td>\n<td>Type of equations<\/td>\n<\/tr>\n<tr>\n<td>x+2=15<\/td>\n<td>One Variable Linear Equation<\/td>\n<\/tr>\n<tr>\n<td>x+9y=10<\/td>\n<td>Two-Variable Linear Equation<\/td>\n<\/tr>\n<tr>\n<td>x+2z2 =35<\/td>\n<td>Non-Linear Equation<\/td>\n<\/tr>\n<tr>\n<td>x7 + 3y =5<\/td>\n<td>Non-Linear Equation<\/td>\n<\/tr>\n<tr>\n<td>4 +2y=18<\/td>\n<td>One Variable Linear Equation<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2><span class=\"ez-toc-section\" id=\"Linear_Equation_Forms\"><\/span>Linear Equation Forms<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Linear equations can be expressed in several forms, including:<\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Standard Form: Ax+By=C<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Slope-Intercept Form: y=mx+c<\/li>\n<\/ul>\n<p>Here, m represents the slope of the line, and c is the y-intercept.<\/p>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Point-Slope Form: y &#8211; y1 = m(x &#8211; x1 )<\/li>\n<\/ul>\n<p>In this form, m is the slope and (x1, y1)  is a specific point on the line.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Methods_to_Solve_the_Linear_Equations\"><\/span>Methods to Solve the Linear Equations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Methods for solving the linear equations are discussed as follows:<\/p>\n<p><b>Graphical Method:<\/b> Plot the given linear equations on a graph to find their point of intersection.<\/p>\n<p><b>Substitution Method:<\/b> Solve one equation for one variable and substitute that into the other equation. This will give you the required solution.<\/p>\n<p><b>Elimination Method:<\/b> Add or subtract the equations to eliminate one variable, making it easier to solve for the other.<\/p>\n<p><b>Cross-Multiplication Method<\/b>: The cross-multiplication method is also a useful method for solving equations in the form of fractions.<\/p>\n<p><b>Determinant Method (Cramer&#8217;s Rule)<\/b>: Determinant Method (Cramer&#8217;s Rule) uses determinants to solve the system of equations.<\/p>\n<p style=\"text-align: center;\"><strong>Also Check: <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/cube\/\">CUBE<\/a><\/strong><\/p>\n<h2><span class=\"ez-toc-section\" id=\"General_Steps_to_Solve_Linear_Equations\"><\/span>General Steps to Solve Linear Equations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Start with simplifying Both Sides. You may combine like terms on both sides of the equation if needed.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Isolate the Variable.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Now move the variable terms to one side of the equation and constant terms to the other side.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">If the variable has a coefficient, divide both sides by this coefficient to solve for the variable.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Substitute the solution back into the original equation to verify that it satisfies the equation.<\/li>\n<\/ul>\n<p><b>Sample Example: <\/b> Solve <b>10y &#8211; 5 = 25 <\/b><\/p>\n<p><b>Solution: <\/b> <b>10y &#8211; 5 = 25 <\/b><\/p>\n<p><b>10y &#8211; 5 + 5 = 25 + 5 <\/b><\/p>\n<p><b>10y  = 30 <\/b><\/p>\n<p><b>y  = 3 <\/b><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Tips_on_Linear_Equations\"><\/span>Tips on Linear Equations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The value of the variable that makes the equation true is called the solution or root.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The equation remains balanced if the same number is added, subtracted, multiplied, or divided on both sides.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">The graph of a linear equation in one or two variables always forms a straight line.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Solved_Examples_of_Linear_Equations\"><\/span>Solved Examples of Linear Equations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><b>Example 1: Solve <\/b><b>5x + 3 = 13<\/b><\/p>\n<p><b>Ans.<\/b> Subtract 3 from both sides:<\/p>\n<p><b>5x + 3 &#8211; 3 = 13 &#8211; 3 <\/b><b> <\/b><\/p>\n<p>Simplifies to:<\/p>\n<p>5x=10<\/p>\n<p>Divide both sides by 5:<\/p>\n<p>x=2<\/p>\n<p><b>Example 2: Solve <\/b><b>2y\u22127=3y+5<\/b><\/p>\n<p><b>Ans.<\/b> Subtract 2y from both sides:<\/p>\n<p>2y\u22127\u22122y=3y+5\u22122y<\/p>\n<p>Simplifies to:<\/p>\n<p>\u22127=y+5<\/p>\n<p>Subtract 5 from both sides:<\/p>\n<p>\u22127\u22125=y+5\u22125<\/p>\n<p>Simplifies to:<\/p>\n<p>\u221212=y<\/p>\n<p>y = -12<\/p>\n<p><b>Example 3: Solve <\/b><b>2z \u2212 5=3z +5<\/b><\/p>\n<p><b>Ans.<\/b> Subtract 2z from both sides:<\/p>\n<p>2z\u22125\u22122z=3z+5\u22122z<\/p>\n<p>Simplifies to:<\/p>\n<p>\u22125 =z+5<\/p>\n<p>Subtract 5 from both sides:<\/p>\n<p>\u22125\u22125=z+5\u22125<\/p>\n<p>Simplifies to:<\/p>\n<p>\u221210=z<\/p>\n<p>z = -10<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Practice_Questions_on_Linear_Equations\"><\/span>Practice Questions on Linear Equations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ol>\n<li>1. Solve the equation: 7x\u22124=10<\/li>\n<li>2. Solve the equation: 3(y+2)=18<\/li>\n<li>3. Solve the equation: 2x+4=3x\u22121<\/li>\n<li>4. Solve for 4\u22123y=2y+1<\/li>\n<li>5. Solve the equation: x2\u200b +1=3<\/li>\n<li>6. Solve the equation: 2z=3z\u22121<\/li>\n<li>7. Solve for 40\u22123y=12y<\/li>\n<li>8. Solve the equation: y2\u200b +1=3<\/li>\n<\/ol>\n<h2><span class=\"ez-toc-section\" id=\"Linear_Equations_FAQs\"><\/span>Linear Equations: FAQs<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_a_linear_equation\"><\/span>What is a linear equation?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tA linear equation is an algebraic expression where each term has a variable raised to the power of 1. It forms a straight line when graphed. Examples include 3x+2=8 and 2x\u2212y=4.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"How_do_you_solve_a_linear_equation_in_one_variable\"><\/span>How do you solve a linear equation in one variable?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tTo solve a linear equation in one variable, isolate the variable by performing inverse operations. For example, if the equation is 4x+5=17, subtract 5 from both sides to get 4x=12, then divide both sides by 4 to find x=3.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"How_can_you_check_if_your_solution_to_a_linear_equation_is_correct\"><\/span>How can you check if your solution to a linear equation is correct?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tTo verify the solution, substitute the value back into the original equation. If both sides of the equation are equal, the solution is correct. For example, if the solution is x=3 for the equation 2x+4=10, substitute 3 in place of x: 2(3)+4=10, which confirms that the solution is correct.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is a linear equation?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A linear equation is an algebraic expression where each term has a variable raised to the power of 1. It forms a straight line when graphed. Examples include 3x+2=8 and 2x\u2212y=4.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How do you solve a linear equation in one variable?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"To solve a linear equation in one variable, isolate the variable by performing inverse operations. For example, if the equation is 4x+5=17, subtract 5 from both sides to get 4x=12, then divide both sides by 4 to find x=3.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"How can you check if your solution to a linear equation is correct?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"To verify the solution, substitute the value back into the original equation. If both sides of the equation are equal, the solution is correct. For example, if the solution is x=3 for the equation 2x+4=10, substitute 3 in place of x: 2(3)+4=10, which confirms that the solution is correct.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>A linear equation is an equation where the highest power of the variable is one. Therefore, a Linear Equation is [&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 Equation","_yoast_wpseo_title":"Linear Equation - Definitions, Types,","_yoast_wpseo_metadesc":"Learn solving linear equations topic of Maths in details explained by subject experts on infinitylearn.com.","custom_permalink":"maths\/linear-equations\/"},"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 Equation - Definitions, Types,<\/title>\n<meta name=\"description\" content=\"Learn solving linear equations 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\/linear-equations\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Linear Equation - 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