{"id":4078,"date":"2022-02-06T19:33:35","date_gmt":"2022-02-06T19:33:35","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=4078"},"modified":"2022-03-01T17:40:34","modified_gmt":"2022-03-01T17:40:34","slug":"how-many-solutions-does-an-equation-have","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/how-many-solutions-does-an-equation-have\/","title":{"rendered":"How Many Solutions Does an Equation Have?"},"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 Many Solutions Does an Equation Have?<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]A system of equations is a set of equations that seek a common solution for the variables included.<\/p>\n<p>Solving a system of equations means finding the values of the variables used in the set of equations. We compute the values of the unknown variables still balancing the equations on both sides. The main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true. A system of linear equations usually has a single solution, but sometimes it can have no solution (parallel lines) or infinite solutions (same line).<\/p>\n<p><strong>One Solution<\/strong>: The solution to the system will be the point where the two lines intersect.<br \/>\n<strong>No Solution<\/strong>: If the system of linear equations have the same slope, the lines are parallel and will never intersect. The system will have no solution.<br \/>\n<strong>Infinite Solutions<\/strong>: If the two lines have the same y-intercept and the slope, they are actually in the same exact line. The system of linear equations will have infinite solutions.[\/vc_column_text][vc_column_text el_class=”headingnew”]Rules[\/vc_column_text][vc_column_text]<strong><a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solutions-of-systems-of-equations\">Determine if given ordered pairs are solution of the system of linear equations in the form of y = mx + b.<\/a><\/strong><br \/>\n1. To solve, substitute the ordered pairs into both equations.<br \/>\n2. The coordinate point is a solution if it makes both equations true.<br \/>\n3. If the coordinate point does not make both equations true, it is not a solution.<\/p>\n<p><a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-linear-systems-of-equations-by-graphing\"><strong>Solve a system of linear equations by graphing:<\/strong><\/a><br \/>\n1. Graph both lines using y-intercept and slopes then find the point of intersection.<br \/>\n2. The point of intersection will be the point where the two lines intersect.<\/p>\n<p><strong><a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-substitution\">Solve system of linear equations by substitution with one variable isolated:<\/a><\/strong><br \/>\nStep 1: Solve one of the equations for one of the variables.<br \/>\nStep 2: Substitute the expression of the isolated variable in the other linear equation.<br \/>\nStep 3: Solve the equation, and you have one of the coordinates of the intersection.<br \/>\nStep 4: Then plug in the value of the coordinate found in step 2 to either equation to find the other coordinate.<\/p>\n<p><a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-elimination\"><strong>Solve a system of linear equations in standard form by elimination:<\/strong><\/a><br \/>\nThe elimination method eliminates one of the variables by adding the equations together.<br \/>\nStep 1: Eliminate one of the variables by adding the equations together.<br \/>\nStep 2: After eliminating one variable, solve for the variable that is left in the equation.<br \/>\nStep 3: 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).<\/p>\n<p><strong><a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-systems-of-equations-by-elimination\">Solve a system of linear equations in standard form by elimination<\/a> (Multiply one of the equations by a constant):<\/strong><br \/>\nIf 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.<br \/>\nThe elimination method eliminates one of the variables by adding the equations together.<\/p>\n<p>Solve the new system by following the three steps:<br \/>\nStep 1: Eliminate one of the variables by adding the equations together.<br \/>\nStep 2: After eliminating one variable, solve for the variable that is left in the equation.<br \/>\nStep 3: 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;\">What is the solution to this system?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solutions-of-systems-of-equations\"><img loading=\"lazy\" class=\"alignnone wp-image-4080 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/1-45.png\" alt=\"\" width=\"337\" height=\"336\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/1-45.png 337w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/1-45-300x300.png 300w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/1-45-150x150.png 150w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/1-45-214x214.png 214w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/a>[\/vc_column_text][vc_column_text el_class=”headingnew”]Solution[\/vc_column_text][vc_column_text]The graphs contain the same slope, and so the lines are parallel and will never intersect. The system will have<span style=\"color: red;\"> <strong>no solution<\/strong><\/span>.[\/vc_column_text][vc_column_text el_class=”headingnew”]Practice How Many Solutions Does an Equation Have?[\/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;\">How many solutions does this system have?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solutions-of-systems-of-equations\"><img loading=\"lazy\" class=\"alignnone wp-image-4083 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/2-35.png\" alt=\" How Many Solutions Does an Equation Have Example - Practice Problem 1\" width=\"306\" height=\"375\" srcset=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/2-35.png 306w, https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/2-35-245x300.png 245w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/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\/solutions-of-systems-of-equations”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][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;\">Is the given ordered pair a solution of the system of linear equations? <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;(5,1)\" alt=\"\\fn_phv (5,1)\" align=\"absmiddle\" \/><\/span><br \/>\n<img style=\"margin-top: 10px; margin-bottom: 9px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;y=-\\frac{2}{5}x+3\" alt=\"\\fn_phv y=-\\frac{2}{5}x+3\" align=\"absmiddle\" \/><br \/>\n<img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;y=3x-5\" alt=\"\\fn_phv y=3x-5\" align=\"absmiddle\" \/><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solutions-of-systems-of-equations\"><img loading=\"lazy\" class=\"alignnone wp-image-3435 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/13-12.png\" alt=\" How Many Solutions Does an Equation Have Example - Practice Problem 2\" width=\"139\" height=\"61\" \/><\/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\/solutions-of-systems-of-equations”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][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;\">Two classmates have decided to read all the volumes in a popular series of books. Mia has already read 10 volumes and will continue to read new ones at a rate of 2 books per week. Sophia, who has not started reading the series yet, will read 3 books per week. If they continue to read at the same pace, after 4 weeks, will they have read the same number of books?<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solutions-of-systems-of-equations\"><img loading=\"lazy\" class=\"alignnone wp-image-3435 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/13-12.png\" alt=\" How Many Solutions Does an Equation Have Example - Practice Problem 3\" width=\"139\" height=\"61\" \/><\/a><br \/>\n<strong>How many books have each of them read?<br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solutions-of-systems-of-equations\"><img loading=\"lazy\" class=\"alignnone wp-image-4086 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/3-27.png\" alt=\"\" width=\"299\" height=\"88\" \/><\/a><br \/>\n<\/strong><\/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\/solutions-of-systems-of-equations”][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=”30px”][vc_row_inner el_class=”boxxborder”][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 4<\/h5>\n<p><strong><span style=\"color: #16a085;\">Amy graphs a line using the equation <img src=\"https:\/\/latex.codecogs.com\/gif.latex?\\fn_phv&space;{\\color{Teal}&space;y=-\\frac{5}{2}x+1}\" alt=\"\\fn_phv {\\color{Teal} y=-\\frac{5}{2}x+1}\" align=\"absmiddle\" \/>. She graphs another line that gives the system the solution <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&space;{\\color{Teal}&space;(-2,6)}\" alt=\"\\fn_phv {\\color{Teal} (-2,6)}\" align=\"absmiddle\" \/>. 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-4090 size-full\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/4-19.png\" alt=\" How Many Solutions Does an Equation Have Example - Practice Problem 4\" width=\"210\" height=\"278\" \/><\/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 height=”30px”][\/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]<strong>Solution<\/strong>: A solution to a system of equations is the value of the variables that make ALL the equations TRUE.<\/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>System<\/strong>: A system is two or more objects that come together to make a group.<\/p>\n<p><strong>System of Linear Equations<\/strong>: A collection of linear equations involving the same set of variables.<\/p>\n<p><strong>Evaluate<\/strong> – to determine or calculate the numerical value.<\/p>\n<p><strong>Slope intercept form<\/strong> \u2013 a linear equation written in the form y = mx + b, where m stands for the slope, and b stands for the y-intercept.<\/p>\n<p><strong>Standard form<\/strong> \u2013 a linear equation written in the form Ax + By = C<\/p>\n<p><strong>Eliminate<\/strong>: To remove or cancel out completely.<\/p>\n<p><strong>Intersect<\/strong>: To cross each other.[\/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\/4th-grade\/graph-points-on-coordinate-plane\"><span style=\"color: #ed5600;\">Graph Points on Coordinate Plane <\/span><\/a><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%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>[\/vc_column_text][vc_column_text el_class=”boxxborder2″ css=”.vc_custom_1635313622279{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\/write-two-step-equations\"><span style=\"color: #333399;\">Write Two-Step Equations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/solve-multi-step-equations\"><span style=\"color: #333399;\">Solve Multi-Step Equations<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/direct-variation-equations-y-mx-\"><span style=\"color: #333399;\">Direct Variation Equations (y = mx)<\/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” 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!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 Many Solutions Does an Equation Have? [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=”headingnew”]Concept[\/vc_column_text][vc_column_text]A system of equations is a set of equations that seek a common solution for the variables included. Solving a system of equations means […]<\/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 Many Solutions Does an Equation Have? | Oryx Learning<\/title>\n<meta name=\"description\" content=\"A system of equations is a set of equations that seek a common solution for the variables included. Solving a system of equations means finding the values of the variables used in the set of equations. 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Solving a system of equations means finding the values of the variables used in the set of equations. 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