{"id":6003,"date":"2022-01-28T17:18:18","date_gmt":"2022-01-28T17:18:18","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=6003"},"modified":"2022-01-28T17:18:18","modified_gmt":"2022-01-28T17:18:18","slug":"how-to-solve-linear-systems-of-equations-by-elimination","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/","title":{"rendered":"How to Solve Linear Systems of Equations by Elimination"},"content":{"rendered":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text]\n<h5>How to Solve Linear Systems of Equations by Elimination<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]In mathematics, a system of equations, also known as a set of simultaneous or an equation system, is a finite set of equations for which we sought the common solutions. A system of equations can be classified in a similar manner as single equations.<\/p>\n<p>Any system of equations can be solved in different methods. To solve a system of equations in 2 variables, we need at least 2 equations. Similarly, for solving a system of equations in 3 variables, we will require at least 3 equations. Let us understand 3 ways to solve a system of equations given the equations are linear equations in two variables.<\/p>\n<p><strong>Substitution Method<\/strong><br \/>\n<strong>Elimination Method<\/strong><br \/>\n<strong>Graphical Method<\/strong><\/p>\n<p>Using the elimination method to solve the system of equations, we eliminate one of the unknowns, by multiplying equations by suitable numbers, so as the coefficients of one of the variables become the same.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]The elimination method eliminates one of the variables by adding the equations together.<\/p>\n<p>If adding the equations together does not eliminate a variable, multiply one of the equations by a constant to make a coefficient in each equation be of opposite values.<\/p>\n<p>Solve the new system by following the three steps:<br \/>\n<strong>Step 1:<\/strong> Eliminate one of the variables by adding the equations together.<br \/>\n<strong>Step 2:<\/strong> After eliminating one variable, solve for the variable that is left in the equation.<br \/>\n<strong>Step 3:<\/strong> After solving for one variable, substitute that value into one of the equations and find the value of the second variable. The values of the two variables is the solution to the system of equations (x,y).[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">Solve the system of linear equations by elimination.<\/span><\/strong><br \/>\n<img style=\"margin-top: 12px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-4x-15y=-17\" alt=\"\\fn_phv -4x-15y=-17\" align=\"absmiddle\" \/><br \/>\n<img style=\"margin-top: 10px; margin-bottom: 0px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;x-5y=13\" alt=\"\\fn_phv x-5y=13\" align=\"absmiddle\" \/>[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]<img style=\"margin-top: 2px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-4x-15y=-17\" alt=\"\\fn_phv -4x-15y=-17\" align=\"absmiddle\" \/><br \/>\n<img style=\"margin-top: 10px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;x-5y=13\" alt=\"\\fn_phv x-5y=13\" align=\"absmiddle\" \/><br \/>\nAdding the equations together does not eliminate a variable. Multiply one of the equations by a constant to make a coefficient in each equation be of opposite values. Choose to multiply by 4 or -3.<br \/>\n<img style=\"margin-top: 11px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-4x-15y=-17\" alt=\"\\fn_phv -4x-15y=-17\" align=\"absmiddle\" \/><br \/>\n<img style=\"margin-top: 11px; margin-bottom: 0px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;4(x-5y=13)\" alt=\"\\fn_phv 4(x-5y=13)\" align=\"absmiddle\" \/><\/p>\n<p>The new system becomes:<br \/>\n<img style=\"margin-top: 11px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-4x-15y=-17\" alt=\"\\fn_phv -4x-15y=-17\" align=\"absmiddle\" \/><br \/>\n<img style=\"margin-top: 12px; margin-bottom: 0px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;4x-20y=52\" alt=\"\\fn_phv 4x-20y=52\" align=\"absmiddle\" \/><\/p>\n<p>Eliminate one of the variables by adding the equations together.<br \/>\n<img style=\"margin-top: 11px; margin-bottom: 1px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-4x-15y=-17\" alt=\"\\fn_phv -4x-15y=-17\" align=\"absmiddle\" \/><br \/>\n<img style=\"margin-top: 11px; margin-bottom: 1px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\underline{\\;\\;\\;4x-20y=52}\" alt=\"\\fn_phv \\underline{\\;\\;\\;4x-20y=52}\" align=\"absmiddle\" \/><br \/>\n<img style=\"margin-top: 5px; margin-bottom: 1px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\underline{\\;\\;\\;\\;\\;\\;\\;\\;-35y=35}\" alt=\"\\fn_phv \\underline{\\;\\;\\;\\;\\;\\;\\;\\;-35y=35}\" align=\"absmiddle\" \/><\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\frac{-35y}{-35}=-\\frac{35}{35}\" alt=\"\\fn_phv \\frac{-35y}{-35}=-\\frac{35}{35}\" align=\"absmiddle\" \/><\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;y=-1\" alt=\"\\fn_phv y=-1\" align=\"absmiddle\" \/><\/p>\n<p>Substitute -1 in for y in either of the equation and solve for the second variable.<br \/>\n<img style=\"margin-top: 11px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-4x-15y=-17\" alt=\"\\fn_phv -4x-15y=-17\" align=\"absmiddle\" \/><br \/>\n<img style=\"margin-top: 11px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-4x-15(-1)=-17\" alt=\"\\fn_phv -4x-15(-1)=-17\" align=\"absmiddle\" \/><br \/>\n<img style=\"margin-top: 11px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-4x+15=-17\" alt=\"\\fn_phv -4x+15=-17\" align=\"absmiddle\" \/><br \/>\n<img style=\"margin-top: 11px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-4x=-32\" alt=\"\\fn_phv -4x=-32\" align=\"absmiddle\" \/><\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\frac{-4x}{-4}=\\frac{-32}{-4}\" alt=\"\\fn_phv \\frac{-4x}{-4}=\\frac{-32}{-4}\" align=\"absmiddle\" \/><\/p>\n<p><img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;x=8\" alt=\"\\fn_phv x=8\" align=\"absmiddle\" \/><\/p>\n<p>The solution is <span style=\"color: #ff0000;\"><strong>(8, -1).<\/strong><\/span>[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice How to Solve Linear Systems of Equations by Elimination[\/vc_column_text][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><strong><span style=\"color: #16a085;\">Solve the system of linear equations by elimination.<\/span><\/strong><br \/>\n<img style=\"margin-top: 11px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;3x-3y=12\" alt=\"\\fn_phv 3x-3y=12\" align=\"absmiddle\" \/><br \/>\n<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;2x+3y=8\" alt=\"\\fn_phv 2x+3y=8\" align=\"absmiddle\" \/><br \/>\n<a href=\"https:\/\/oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-elimination\"><img loading=\"lazy\" class=\"alignnone wp-image-6005 size-full\" style=\"margin-top: 10px; margin-bottom: 1px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/12\/table-temp.png\" alt=\"\" width=\"151\" height=\"55\" \/><\/a><br \/>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-elimination”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><strong><span style=\"color: #16a085;\">Solve the system of linear equations by elimination.<\/span><\/strong><br \/>\n<img style=\"margin-top: 11px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;3x+y=1\" alt=\"\\fn_phv 3x+y=1\" align=\"absmiddle\" \/><br \/>\n<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-2x-4y=16\" alt=\"\\fn_phv -2x-4y=16\" align=\"absmiddle\" \/><br \/>\n<a href=\"https:\/\/oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-elimination\"><img loading=\"lazy\" class=\"alignnone wp-image-6005 size-full\" style=\"margin-top: 10px; margin-bottom: 1px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/12\/table-temp.png\" alt=\"\" width=\"151\" height=\"55\" \/><\/a>[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-elimination”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">Solve the system of linear equations by elimination.<\/span><\/strong><br \/>\n<img style=\"margin-top: 11px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-4x-15y=-17\" alt=\"\\fn_phv -4x-15y=-17\" align=\"absmiddle\" \/><br \/>\n<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;\\;\\;\\;x-5y=13\" alt=\"\\fn_phv \\;\\;\\;x-5y=13\" align=\"absmiddle\" \/><br \/>\n<a href=\"https:\/\/oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-elimination\"><img loading=\"lazy\" class=\"alignnone wp-image-6005 size-full\" style=\"margin-top: 10px; margin-bottom: 1px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/12\/table-temp.png\" alt=\"\" width=\"151\" height=\"55\" \/><\/a><br \/>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-elimination”][\/vc_column_inner][\/vc_row_inner][vc_empty_space][\/vc_column][vc_column width=”1\/3″ css=”.vc_custom_1633369011398{margin-bottom: 50px !important;}”][vc_row_inner el_class=”stickynotee”][vc_column_inner][vc_single_image image=”2265″ img_size=”full” alignment=”center” css_animation=”fadeIn” css=”.vc_custom_1633509989314{border-radius: 10px !important;}” el_class=”stickypin”][vc_column_text]A <strong>system of linear equations<\/strong> – is a set of equations which are satisfied by the same set of variables.<\/p>\n<p><strong>Variable<\/strong> – A symbol, usually a letter, used to represent a number in mathematical expressions or sentences.<\/p>\n<p><strong>Equation<\/strong> – A mathematical sentence stating that two quantities are equal.<\/p>\n<p><strong>Slope intercept form<\/strong> \u2013 a linear equation written in the form <strong>y = mx + b<\/strong>, where <strong>m<\/strong> stands for the slope, and <strong>b<\/strong> stands for the y-intercept.<\/p>\n<p><strong>Standard form<\/strong> \u2013 a linear equation written in the form <strong>Ax + By = C<\/strong><\/p>\n<p><strong>Solution<\/strong> – A solution to a system of equations is the value of the variables that makes ALL the equations True.<\/p>\n<p><strong>Eliminate<\/strong> – To remove or cancel out completely.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”boxxborder2″]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-equations-with-rational-coefficients\"><span style=\"color: #ed5600;\">Solve Equations with Rational Coefficients<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-two-step-equations\"><span style=\"color: #ed5600;\">Solve Two-Step Equations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/write-two-step-equations\"><span style=\"color: #ed5600;\">Write Two-Step Equations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/Solve%20Two-Sided%20Equations%20with%20Rational%20Coefficients\"><span style=\"color: #ed5600;\">Solve Two-Sided Equations with Rational Coefficients<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-multi-step-equations\"><span style=\"color: #ed5600;\">Solve Multi-Step Equations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/slope-intercept-form-of-an-equation\"><span style=\"color: #ed5600;\">Slope-intercept Form of an Equation<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/graphing-lines-using-intercepts\"><span style=\"color: #ed5600;\">Graphing Lines Using Intercepts<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/write-linear-equations\"><span style=\"color: #ed5600;\">Write Linear Equations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/direct-variation-equations-y-mx-\"><span style=\"color: #ed5600;\">Direct Variation Equations (y = mx)<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solutions-of-systems-of-equations\"><span style=\"color: #ed5600;\">Solutions of Systems of Equations<\/span><\/a>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1638344431036{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 35px !important;}”]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-substitution\"><span style=\"color: #333399;\">Solve Systems of Equations by Substitution<\/span><\/a><br \/>\n<a href=\"https:\/\/oryxlearning.com\/question\/maths\/8th-grade\/solve-linear-systems-of-equations-by-graphing\"><span style=\"color: #333399;\">Solve Linear Systems of Equations by Graphing<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/applications-of-systems\"><span style=\"color: #333399;\">Applications of Systems<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/representing-relationships\"><span style=\"color: #333399;\">Representing Relationships<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/relations\"><span style=\"color: #333399;\">Relations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/functions\"><span style=\"color: #333399;\">Functions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/linear-functions\"><span style=\"color: #333399;\">Linear Functions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/linear-and-nonlinear-functions\"><span style=\"color: #333399;\">Linear and Nonlinear Functions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/quadratic-functions\"><span style=\"color: #333399;\">Quadratic Functions<\/span><\/a>[\/vc_column_text][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Grade 1″ color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F1st-grade%2Fmaths|title:Grade%201%20Math||”][vc_btn title=”Grade 2″ color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F2nd-grade%2Fmaths|title:Grade%202%20Math||”][vc_btn title=”Grade 3″ color=”violet” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F3rd-grade%2Fmaths|title:Grade%203%20Math||”][vc_btn title=”Grade 4″ color=”blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F4th-grade%2Fmaths|title:Grade%204%20Math||”][vc_btn title=”Grade 5″ color=”green” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F5th-grade%2Fmaths|title:Grade%205%20Math||”][vc_btn title=”Grade 6″ color=”info” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F6th-grade%2Fmaths|title:Grade%206%20Math||”][vc_btn title=”Grade 7″ color=”vista-blue” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F7th-grade%2Fmaths|title:Grade%207%20Math||”][vc_btn title=”Grade 8″ color=”mulled-wine” link=”url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F8th-grade%2Fmaths|title:Grade%208%20Math||”][\/vc_column_inner][\/vc_row_inner][vc_row_inner equal_height=”yes” el_class=”btninlinespacing”][vc_column_inner][vc_btn title=”Geometry and Spatial sense” color=”warning” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Fgeometry-and-spatial-sense|title:Geometry%20and%20Spatial%20sense||”][vc_btn title=”Graphs” color=”danger” link=”url:https%3A%2F%2Foryxlearning.com%2Ftopics%2Fmaths%2Fgraphs|title:Graphs||”][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][\/vc_section]\n","protected":false},"excerpt":{"rendered":"<p>[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] How to Solve Linear Systems of Equations by Elimination [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]In mathematics, a system of equations, also known as a set of simultaneous or an equation system, is a finite set of […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How to Solve Linear Systems of Equations by Elimination | Oryx Learning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How to Solve Linear Systems of Equations by Elimination\" \/>\n<meta property=\"og:description\" content=\"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] How to Solve Linear Systems of Equations by Elimination [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]In mathematics, a system of equations, also known as a set of simultaneous or an equation system, is a finite set of […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/\" \/>\n<meta property=\"og:site_name\" content=\"Oryx Learning\" \/>\n<meta property=\"og:image\" content=\"https:\/\/latex.codecogs.com\/svg.latex?fn_phv&space;-4x-15y=-17\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"9 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Organization\",\"@id\":\"https:\/\/oryxlearning.com\/learn\/#organization\",\"name\":\"Oryx Learning\",\"url\":\"https:\/\/oryxlearning.com\/learn\/\",\"sameAs\":[],\"logo\":{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/oryxlearning.com\/learn\/#logo\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/Oryx-Learning-Logo-3.png\",\"contentUrl\":\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/Oryx-Learning-Logo-3.png\",\"width\":150,\"height\":74,\"caption\":\"Oryx Learning\"},\"image\":{\"@id\":\"https:\/\/oryxlearning.com\/learn\/#logo\"}},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/oryxlearning.com\/learn\/#website\",\"url\":\"https:\/\/oryxlearning.com\/learn\/\",\"name\":\"Oryx Learning\",\"description\":\"Complete interactive math curriculum\",\"publisher\":{\"@id\":\"https:\/\/oryxlearning.com\/learn\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/oryxlearning.com\/learn\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"ImageObject\",\"@id\":\"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/#primaryimage\",\"inLanguage\":\"en-US\",\"url\":\"https:\/\/latex.codecogs.com\/svg.latex?\\\\fn_phv&space;-4x-15y=-17\",\"contentUrl\":\"https:\/\/latex.codecogs.com\/svg.latex?\\\\fn_phv&space;-4x-15y=-17\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/#webpage\",\"url\":\"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/\",\"name\":\"How to Solve Linear Systems of Equations by Elimination | Oryx Learning\",\"isPartOf\":{\"@id\":\"https:\/\/oryxlearning.com\/learn\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/#primaryimage\"},\"datePublished\":\"2022-01-28T17:18:18+00:00\",\"dateModified\":\"2022-01-28T17:18:18+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/oryxlearning.com\/learn\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"How to Solve Linear Systems of Equations by Elimination\"}]}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"How to Solve Linear Systems of Equations by Elimination | Oryx Learning","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/","og_locale":"en_US","og_type":"article","og_title":"How to Solve Linear Systems of Equations by Elimination","og_description":"[vc_section full_width=”stretch_row” content_placement=”middle” css=”.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}” el_id=”bg-sec”][vc_row full_width=”stretch_row_content” el_class=”faaaq”][vc_column width=”1\/12″][\/vc_column][vc_column width=”1\/2″][vc_row_inner content_placement=”middle” el_class=”topheadingg”][vc_column_inner width=”1\/6″][vc_single_image image=”2283″ img_size=”full”][\/vc_column_inner][vc_column_inner width=”5\/6″][vc_column_text] How to Solve Linear Systems of Equations by Elimination [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]In mathematics, a system of equations, also known as a set of simultaneous or an equation system, is a finite set of […]","og_url":"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/","og_site_name":"Oryx Learning","og_image":[{"url":"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-4x-15y=-17"}],"twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"9 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/oryxlearning.com\/learn\/#organization","name":"Oryx Learning","url":"https:\/\/oryxlearning.com\/learn\/","sameAs":[],"logo":{"@type":"ImageObject","@id":"https:\/\/oryxlearning.com\/learn\/#logo","inLanguage":"en-US","url":"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/Oryx-Learning-Logo-3.png","contentUrl":"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/Oryx-Learning-Logo-3.png","width":150,"height":74,"caption":"Oryx Learning"},"image":{"@id":"https:\/\/oryxlearning.com\/learn\/#logo"}},{"@type":"WebSite","@id":"https:\/\/oryxlearning.com\/learn\/#website","url":"https:\/\/oryxlearning.com\/learn\/","name":"Oryx Learning","description":"Complete interactive math curriculum","publisher":{"@id":"https:\/\/oryxlearning.com\/learn\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/oryxlearning.com\/learn\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/#primaryimage","inLanguage":"en-US","url":"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-4x-15y=-17","contentUrl":"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;-4x-15y=-17"},{"@type":"WebPage","@id":"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/#webpage","url":"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/","name":"How to Solve Linear Systems of Equations by Elimination | Oryx Learning","isPartOf":{"@id":"https:\/\/oryxlearning.com\/learn\/#website"},"primaryImageOfPage":{"@id":"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/#primaryimage"},"datePublished":"2022-01-28T17:18:18+00:00","dateModified":"2022-01-28T17:18:18+00:00","breadcrumb":{"@id":"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-elimination\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/oryxlearning.com\/learn\/"},{"@type":"ListItem","position":2,"name":"How to Solve Linear Systems of Equations by Elimination"}]}]}},"_links":{"self":[{"href":"https:\/\/oryxlearning.com\/learn\/wp-json\/wp\/v2\/pages\/6003"}],"collection":[{"href":"https:\/\/oryxlearning.com\/learn\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/oryxlearning.com\/learn\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/oryxlearning.com\/learn\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/oryxlearning.com\/learn\/wp-json\/wp\/v2\/comments?post=6003"}],"version-history":[{"count":4,"href":"https:\/\/oryxlearning.com\/learn\/wp-json\/wp\/v2\/pages\/6003\/revisions"}],"predecessor-version":[{"id":6055,"href":"https:\/\/oryxlearning.com\/learn\/wp-json\/wp\/v2\/pages\/6003\/revisions\/6055"}],"wp:attachment":[{"href":"https:\/\/oryxlearning.com\/learn\/wp-json\/wp\/v2\/media?parent=6003"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}