{"id":5966,"date":"2022-01-28T19:04:59","date_gmt":"2022-01-28T19:04:59","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=5966"},"modified":"2022-03-03T13:17:36","modified_gmt":"2022-03-03T13:17:36","slug":"how-to-solve-linear-systems-of-equations-by-graphing","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/how-to-solve-linear-systems-of-equations-by-graphing\/","title":{"rendered":"How to Solve Linear Systems of Equations by Graphing"},"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 Graphing<\/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>In the graphical method, the solution of simultaneous equations is obtained by plotting their graphs. The point of intersection of the two lines is the solution of the system of equations using graphical method.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]1. Make sure both equations are in slope-intercept form. If any or both equations are in standard form, convert them into slope-intercept form.<br \/>\n2. Graph both lines using y-intercept and slopes then find the point of intersection.<br \/>\n3. The point of intersection will be the point where the two lines intersect.<br \/>\n4. If the lines are parallel then there is no solution as parallel lines can never intersect.<br \/>\n5. If the lines lie on top of each other, there are infinite solutions.[\/vc_column_text][vc_column_text el_class=”headingnew”]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">What is the solution to the following system?<\/span><\/strong><br \/>\n<img style=\"margin-top: 12px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;x+y=3\" alt=\"\\fn_phv x+y=3\" align=\"absmiddle\" \/><br \/>\n<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;y=-3(2x-1)\" alt=\"\\fn_phv y=-3(2x-1)\" align=\"absmiddle\" \/><\/p>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]1. Change the first equation into slope-intercept form.<br \/>\n<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;y=-x+3\" alt=\"\\fn_phv y=-x+3\" align=\"absmiddle\" \/><\/p>\n<p>2. Graph both lines using y-intercept and slopes then find the point of intersection.<\/p>\n<p>3. The point of intersection will be the point where the two lines intersect.<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-linear-systems-of-equations-by-graphing\"><img loading=\"lazy\" class=\"alignnone wp-image-5968 size-full\" style=\"margin-top: 12px; margin-bottom: 12px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/graph.png\" alt=\"\" width=\"295\" height=\"294\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/graph.png 295w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/graph-150x150.png 150w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/graph-214x214.png 214w\" sizes=\"(max-width: 295px) 100vw, 295px\" \/><\/a><br \/>\nThe solution to the system is <span style=\"color: #ff0000;\"><strong>(0, 3)<\/strong><\/span><br \/>\n[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice How to Solve Linear Systems of Equations by Graphing[\/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;\">What is the solution to the following system?<\/span><\/strong><br \/>\n<img style=\"margin-top: 8px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;2x&space;+&space;y&space;=&space;0\" alt=\"\\fn_phv 2x + y = 0\" align=\"absmiddle\" \/><br \/>\n<img style=\"margin-top: 8px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;5x&space;+&space;2y&space;=&space;2\" alt=\"\\fn_phv 5x + 2y = 2\" align=\"absmiddle\" \/><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-linear-systems-of-equations-by-graphing\"><img loading=\"lazy\" class=\"alignnone wp-image-5970 size-full\" style=\"margin-top: 10px; margin-bottom: 1px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/Solution.png\" alt=\"\" width=\"156\" height=\"203\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-linear-systems-of-equations-by-graphing”][\/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;\">What is the solution to the following system?<\/span><\/strong><br \/>\n<img style=\"margin-top: 10px; margin-bottom: 0px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;y&space;=&space;-\\frac{11}{5}x+6\" alt=\"\\fn_phv y = -\\frac{11}{5}x+6\" align=\"absmiddle\" \/><br \/>\n<img style=\"margin-top: 10px; margin-bottom: 0px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;3x&space;-&space;5y&space;=&space;40\" alt=\"\\fn_phv 3x - 5y = 40\" align=\"absmiddle\" \/><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-linear-systems-of-equations-by-graphing\"><img loading=\"lazy\" class=\"alignnone wp-image-5970 size-full\" style=\"margin-top: 10px; margin-bottom: 1px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/Solution.png\" alt=\" Solve systems of equations by graphing (Pre-Algebra, Graphing and functions) - Practice Problem 2\" width=\"156\" height=\"203\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-linear-systems-of-equations-by-graphing”][\/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;\">Betty graphed a line using the equation <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;{\\color{Teal}&space;y=\\frac{1}{2}x-3}\" alt=\"\\fn_phv {\\color{Teal} y=\\frac{1}{2}x-3}\" align=\"absmiddle\" \/>. She graphs another line that yields infinite solutions. Which line could be the second line that she graphed?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-linear-systems-of-equations-by-graphing\"><img loading=\"lazy\" class=\"alignnone wp-image-5972 size-full\" style=\"margin-top: 13px; margin-bottom: 1px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/11\/graphing.png\" alt=\" Solve systems of equations by graphing (Pre-Algebra, Graphing and functions) - Practice Problem 3\" width=\"175\" height=\"273\" \/><\/a><\/p>\n[\/vc_column_text][vc_single_image image=”2159″ img_size=”full” alignment=”right” onclick=”custom_link” link=”https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-linear-systems-of-equations-by-graphing”][\/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>Coordinate Point<\/strong> – A pair of numbers used to locate a point in the coordinate plane.<\/p>\n<p><strong>Coordinate Plane<\/strong> – A coordinate system in which a horizontal number line and a vertical number line intersect at their zero points.<\/p>\n<p><strong>Intersect <\/strong>– To cross each other.<\/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.[\/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_1638277052703{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:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-elimination\"><span style=\"color: #333399;\">Solve Systems of Equations by Elimination<\/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” 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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 Graphing [\/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 Graphing | Oryx 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