{"id":37735,"date":"2023-08-23T11:34:35","date_gmt":"2023-08-23T17:04:35","guid":{"rendered":"https:\/\/therightmentor.com\/?p=37735"},"modified":"2024-06-13T19:20:22","modified_gmt":"2024-06-13T13:50:22","slug":"linear-equations-in-two-variables-study","status":"publish","type":"post","link":"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/linear-equations-in-two-variables-study\/","title":{"rendered":"LINEAR EQUATIONS IN TWO VARIABLES | Study"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 ez-toc-wrap-center counter-hierarchy ez-toc-counter ez-toc-light-blue ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title ez-toc-toggle\" style=\"cursor:pointer\">Click For 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\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><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><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/linear-equations-in-two-variables-study\/#Pre-Requisires\" >Pre-Requisires<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/linear-equations-in-two-variables-study\/#Linear_Equations_in_Two_Variables_Speed_Notes\" >Linear Equations in Two Variables | Speed Notes<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/linear-equations-in-two-variables-study\/#Study_Tools\" >Study Tools<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/linear-equations-in-two-variables-study\/#Dig_Deep\" >Dig Deep<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/linear-equations-in-two-variables-study\/#Sub_%E2%80%93_Topics\" >Sub &#8211; Topics<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/linear-equations-in-two-variables-study\/#Chapters_Index\" >Chapters Index<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/therightmentor.com\/trm-course\/home\/courses\/cbse-9-mathematics-study-premium\/linear-equations-in-two-variables-study\/#Assessments\" >Assessments<\/a><\/li><\/ul><\/nav><\/div>\n\n<hr class=\"wp-block-separator alignfull has-text-color has-vivid-cyan-blue-color has-alpha-channel-opacity has-vivid-cyan-blue-background-color has-background is-style-wide is-style-wide--1\"\/>\n\n\n\n<div class=\"wp-block-group alignfull has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group alignfull has-tertiary-background-color has-background has-global-padding is-layout-constrained wp-container-core-group-is-layout-19c400f2 wp-block-group-is-layout-constrained\" style=\"margin-top:0;margin-bottom:0\">\n<div class=\"wp-block-buttons alignfull is-content-justification-left is-layout-flex wp-container-core-buttons-is-layout-6e9f73ed wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-base-color has-vivid-red-background-color has-text-color has-background wp-element-button\" href=\"https:\/\/therightmentor.com\/number-systems-assessments\/\">Assess<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-vivid-cyan-blue-background-color has-background wp-element-button\" style=\"border-width:2px\">Interact<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-group alignfull has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-columns alignfull is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-tertiary-background-color has-background is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:33.33%\">\n<h2 class=\"wp-block-heading has-large-font-size\"><span class=\"ez-toc-section\" id=\"Pre-Requisires\"><\/span>Pre-Requisires<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-small-font-size\">Test &amp; Enrich<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button has-custom-width wp-block-button__width-100 has-custom-font-size is-style-outline has-small-font-size is-style-outline--2\"><a class=\"wp-block-button__link has-text-align-left wp-element-button\">Pre &#8211; Requisite<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:66.66%\">\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"Linear Equations in two variables\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/qxQ7kV3Z-e8?list=PLEuUy4TjqFeAOkz9COEMEDiOCqPLFgr-9\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><figcaption class=\"wp-element-caption\">English Version<\/figcaption><\/figure>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-columns alignfull is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column has-base-background-color has-text-color has-background has-link-color wp-elements-95ef6b2090c5f98d220c9b89e2005ec0 is-layout-flow wp-block-column-is-layout-flow\" style=\"color:#000000;padding-top:2em;padding-right:2em;padding-bottom:2em;padding-left:2em\">\n<h2 class=\"wp-block-heading\" id=\"single\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Linear_Equations_in_Two_Variables_Speed_Notes\"><\/span><strong>Linear Equations in Two Variables | Speed Notes<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-luminous-vivid-orange-color has-text-color has-normal-font-size\" style=\"line-height:1.5\"><strong><strong>Notes For Quick Recap<\/strong><\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-css-opacity has-background is-style-wide is-style-wide--3\" style=\"background-color:#000000;color:#000000\"\/>\n\n\n\n<div class=\"wp-block-group has-medium-font-size is-layout-flow wp-block-group-is-layout-flow\">\n<p><strong>Linear Equations<\/strong><\/p>\n\n\n\n<p>The equation of a straight line is the linear equation. It could be in one variable or two variables.<\/p>\n\n\n\n<p><strong>Linear Equation in One Variable<\/strong><\/p>\n\n\n\n<p>The equation with one variable in it is known as a Linear Equation in One Variable. <strong>(Scroll down to continue &#8230;)<\/strong><\/p>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"single\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Study_Tools\"><\/span><strong>Study Tools<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-luminous-vivid-orange-color has-text-color has-normal-font-size\" style=\"line-height:1.5\"><strong>Audio, Visual &amp; Digital Content<\/strong><\/p>\n\n\n                <div class=\"igd igd-shortcode-wrap igd-shortcode-slider\"\n                     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                    style=\"--module-width: 100%; --module-height: ;\"\n                ><\/div>\n                \n\n\n\n<div class=\"wp-block-group has-medium-font-size is-layout-flow wp-block-group-is-layout-flow\">\n<p>The general form for <strong>Linear Equation in One Variable <\/strong>is px + q = s, where p, q and s are real numbers and p \u2260 0.<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>x + 5 = 10<\/p>\n\n\n\n<p>y \u2013 3 = 19<\/p>\n\n\n\n<p>These are called Linear Equations in One Variable because the highest degree of the variable is one.<\/p>\n\n\n\n<p><strong>Graph of the Linear Equation in One Variable<\/strong><\/p>\n\n\n\n<p>We can mark the point of the linear equation in one variable on the number line.<\/p>\n\n\n\n<p>x = 2 can be marked on the number line as follows &#8211;<\/p>\n\n\n\n<p>Graph of the Linear Equation in One Variable<\/p>\n\n\n\n<p><strong>Linear Equation in Two Variables<\/strong><\/p>\n\n\n\n<p>An equation with two variables is known as a Linear Equation in Two Variables. The general form of the linear equation in two variables is<\/p>\n\n\n\n<p>ax + by + c = 0<\/p>\n\n\n\n<p>where a and b are coefficients and c is the constant. a \u2260 0 and b \u2260 0.<\/p>\n\n\n\n<p><strong>Example<\/strong><\/p>\n\n\n\n<p>6x + 2y + 5 = 0, etc.<\/p>\n\n\n\n<p><strong>Slope Intercept form<\/strong><\/p>\n\n\n\n<p>Generally, the linear equation in two variables is written in the slope-intercept form as this is the easiest way to find the slope of the straight line while drawing the graph of it.<\/p>\n\n\n\n<p>The slope-intercept form is y = mx+c<\/p>\n\n\n\n<p>Where m represents the slope of the line.<\/p>\n\n\n\n<p>and c tells the point of intersection of the line with the y-axis.<\/p>\n\n\n\n<p><strong>Remark<\/strong>: If b = 0 i.e. if the equation is y = mx then the line will pass through the origin as the y-intercept is zero.<\/p>\n\n\n\n<p><strong>Solution of a Linear Equation<\/strong><\/p>\n\n\n\n<p>There is only one solution in the linear equation in one variable but there are infinitely many solutions in the linear equation in two variables.<\/p>\n\n\n\n<p>As there are two variables, the solution will be in the form of an ordered pair, i.e. (x, y).<\/p>\n\n\n\n<p>The pair which satisfies the equation is the solution to that particular equation.<\/p>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>Find the solution for the equation 2x + y = 7.<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>To calculate the solution of the given equation we will take x = 0<\/p>\n\n\n\n<p>2(0) + y = 7<\/p>\n\n\n\n<p>y = 7<\/p>\n\n\n\n<p>Hence, one solution is (0, 7).<\/p>\n\n\n\n<p>To find another solution we will take y = 0<\/p>\n\n\n\n<p>2x + 0 = 7<\/p>\n\n\n\n<p>x = 3.5<\/p>\n\n\n\n<p>So another solution is (3.5, 0).<\/p>\n\n\n\n<p>Graph of a Linear Equation in Two Variables<\/p>\n\n\n\n<p>To draw the graph of a linear equation in two variables, we need to draw a table to write the solutions of the given equation, and then plot them on the Cartesian plane.<\/p>\n\n\n\n<p>By joining these coordinates, we get the line of that equation.<\/p>\n\n\n\n<p>The coordinates which satisfy the given Equation lie on the line of the equation.<\/p>\n\n\n\n<p>Every point (x, y) on the line is the solution x = a, y = b of the given Equation.<\/p>\n\n\n\n<p>Any point, which does not lie on the line AB, is not a solution of Equation.<\/p>\n\n\n\n<p>Example:<\/p>\n\n\n\n<p>Draw the graph of the equation 3x + 4y = 12.<\/p>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<p>To draw the graph of the equation 3x + 4y = 12, we need to find the solutions of the equation.<\/p>\n\n\n\n<p>Let x = 0<\/p>\n\n\n\n<p>3(0) + 4y = 12<\/p>\n\n\n\n<p>y = 3<\/p>\n\n\n\n<p>Let y = 0<\/p>\n\n\n\n<p>3x + 4(0) = 12<\/p>\n\n\n\n<p>x = 4<\/p>\n\n\n\n<p>Now draw a table to write the solutions.<\/p>\n\n\n\n<p>x 0 4<\/p>\n\n\n\n<p>y 3 0<\/p>\n\n\n\n<p>Now we can draw the graph easily by plotting these points on the Cartesian plane.<\/p>\n\n\n\n<p><strong>Linear Equation in Two Variables<\/strong><\/p>\n\n\n\n<p>Equations of Lines Parallel to the x-axis and y-axis<\/p>\n\n\n\n<p>When we draw the graph of the linear equation in one variable then it will be a point on the number line.<\/p>\n\n\n\n<p>x &#8211; 5 = 0<\/p>\n\n\n\n<p>x = 5<\/p>\n\n\n\n<p>This shows that it has only one solution i.e. x = 5, so it can be plotted on the number line.<\/p>\n\n\n\n<p>But if we treat this equation as the linear equation in two variables then it will have infinitely many solutions and the graph will be a straight line.<\/p>\n\n\n\n<p>x \u2013 5 = 0 or x + (0) y \u2013 5 = 0<\/p>\n\n\n\n<p>This shows that this is the linear equation in two variables where the value of y is always zero. So the line will not touch the y-axis at any point.<\/p>\n\n\n\n<p>x = 5, x = number, then the graph will be the vertical line parallel to the y-axis.<\/p>\n\n\n\n<p>All the points on the line will be the solution of the given equation.<\/p>\n\n\n\n<p>Equations of Lines Parallel to the x-axis and y-axis<\/p>\n\n\n\n<p>Similarly if y = &#8211; 3, y = number then the graph will be the horizontal line parallel to the x-axis.<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-uagb-container uagb-block-fe53acc0 alignfull uagb-is-root-container\"><div class=\"uagb-container-inner-blocks-wrap\">\n<div class=\"wp-block-uagb-container uagb-block-f7936561\">\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-4-3 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe title=\"Volume\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/dy2ZsRQqK0M?list=PLEuUy4TjqFeAOkz9COEMEDiOCqPLFgr-9\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe>\n<\/div><figcaption class=\"wp-element-caption\">Hindi Version<\/figcaption><\/figure>\n<\/div>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-columns alignfull is-layout-flex wp-container-core-columns-is-layout-d2da2050 wp-block-columns-is-layout-flex\" style=\"margin-bottom:0\">\n<div class=\"wp-block-column has-tertiary-background-color has-text-color has-background has-link-color wp-elements-2e5ac2404643eed0228dee617e0c2bd5 is-layout-flow wp-block-column-is-layout-flow\" style=\"color:#000000;padding-top:2em;padding-right:2em;padding-bottom:2em;padding-left:2em\">\n<h2 class=\"wp-block-heading\" id=\"family\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Dig_Deep\"><\/span><strong>Dig Deep<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-luminous-vivid-orange-color has-text-color has-normal-font-size\" style=\"line-height:1.5\"><strong>Topic Level Resources<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity is-style-wide is-style-wide--4\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-28f84493 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-d2da2050 wp-block-columns-is-layout-flex\" style=\"margin-bottom:0\">\n<div class=\"wp-block-column has-text-color has-background has-link-color wp-elements-c7db55dbe9ca946a40cc845611f21236 is-layout-flow wp-block-column-is-layout-flow\" style=\"color:#000000;background-color:#c0ebf1;padding-top:2em;padding-right:2em;padding-bottom:2em;padding-left:2em\">\n<h2 class=\"wp-block-heading\" id=\"patron\" style=\"font-size:clamp(24.034px, 1.502rem + ((1vw - 3.2px) * 1.565), 40px);\"><span class=\"ez-toc-section\" id=\"Sub_%E2%80%93_Topics\"><\/span><strong>Sub &#8211; Topics<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p class=\"has-normal-font-size\"><strong>Select A Topic<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity is-style-wide is-style-wide--5\"\/>\n\n\n\n<p class=\"has-medium-font-size\">Topic: <\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-d2da2050 wp-block-columns-is-layout-flex\" style=\"margin-bottom:0\">\n<div class=\"wp-block-column has-text-color has-background has-link-color has-medium-font-size wp-elements-cbc7d8945c2bc94b3a25d36303f59d82 is-layout-flow wp-block-column-is-layout-flow\" 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style=\"display:block;border-radius:999px;\" xml:space=\"preserve\"><g><path fill=\"#fff\" d=\"M18 14V8h-4v6H8v4h6v6h4v-6h6v-4h-6z\" fill-rule=\"evenodd\"><\/path><\/g><\/svg><\/span><\/a><\/div><div class=\"heateorSssClear\"><\/div><\/div><div class='heateorSssClear'><\/div><br\/><p>Pre-Requisires Test &amp; Enrich Linear Equations in Two Variables | Speed Notes Notes For Quick Recap Linear Equations The equation of a straight line is the linear equation. 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