{"id":102,"date":"2022-04-13T09:59:46","date_gmt":"2022-04-13T09:59:46","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=102"},"modified":"2025-03-05T10:24:16","modified_gmt":"2025-03-05T10:24:16","slug":"e-2-solve-a-pair-of-equations-by-graphing","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/e-2-solve-a-pair-of-equations-by-graphing\/","title":{"rendered":"E.2 Solve a pair of equations by graphing"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Solve a pair of equations by graphing<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-4dde4300b7763c9a2a860fe18546dfe2\" style=\"color:#74008b;text-transform:uppercase\">key notes:<\/p>\n\n\n\n<h4 class=\"wp-block-heading has-foreground-color has-text-color\" id=\"yui_3_18_1_1_1670028809318_7279\">Solving&nbsp;systems&nbsp;of&nbsp;linear&nbsp; equations:<\/h4>\n\n\n\n<p class=\"has-large-font-size\">You&nbsp;can solve systems of equations in a few different&nbsp;ways.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\" id=\"yui_3_18_1_1_1670028809318_7272\"><strong>Graphing:<\/strong><\/h4>\n\n\n\n<p class=\"has-large-font-size\">You&nbsp;can solve systems of equations by graphing. Look for the point where the lines&nbsp;intersect.<\/p>\n\n\n\n<p class=\"has-large-font-size\">Let&#8217;s&nbsp;try it! Solve the system of linear&nbsp;equations.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">y=3x+7<\/li>\n\n\n\n<li class=\"has-large-font-size\">y=\u20134x<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">Start&nbsp;by graphing the first equation,&nbsp;y=3x+7.&nbsp;Since this equation is in&nbsp;slope-intercept&nbsp;form,&nbsp;you can graph the line by plotting the&nbsp;<em>y<\/em>-intercept,&nbsp;7, and then using the slope,&nbsp;3.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-45.png\" alt=\"\" class=\"wp-image-11783\" style=\"width:492px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-45.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-45-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-45-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-45-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\">Now,&nbsp;graph the second equation,&nbsp;y=\u20134x,&nbsp;on the same coordinate plane. You can graph the line by plotting the&nbsp;<em>y<\/em>-intercept,&nbsp;0, and then using the slope,&nbsp;\u20134.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-46.png\" alt=\"\" class=\"wp-image-11788\" style=\"width:479px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-46.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-46-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-46-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-46-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\">Last,&nbsp;find the point where the lines&nbsp;intersect.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-47.png\" alt=\"\" class=\"wp-image-11791\" style=\"width:486px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-47.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-47-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-47-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-47-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p class=\"has-large-font-size\">So,&nbsp;the solution to this system of equations is&nbsp;(\u20131,4).<\/p>\n\n\n\n<p class=\"has-large-font-size\">You&nbsp;can check that this answer is correct by substituting&nbsp;\u20131&nbsp;for&nbsp;<em>x<\/em>&nbsp;and 4 for&nbsp;<em>y<\/em>&nbsp;into the original&nbsp;equations.<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li class=\"has-large-font-size\">y=3x+7<\/li>\n\n\n\n<li class=\"has-large-font-size\">4=3(\u20131)+7<\/li>\n\n\n\n<li class=\"has-large-font-size\">4=\u20133+7<\/li>\n\n\n\n<li>4=4<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>y=\u20134x<\/li>\n\n\n\n<li>4=\u20134(\u20131)<\/li>\n\n\n\n<li>4=4<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">Since&nbsp;both equations are true,&nbsp;(\u20131,4)&nbsp;is the solution to the system of&nbsp;equations.<\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e9a3a3\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-85b33ed06fbe38d46c78bde1d6f11a70\" style=\"color:#b00012\">Solve these simultaneous equations by graphing.<\/p>\n\n\n\n<p> First graph the equations, and then type the solution.<br>y=2x+3<br>y=x<br>Click to select points on the graph.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-24-3.png\" alt=\"\" class=\"wp-image-11793\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-24-3.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-24-3-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-24-3-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-24-3-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p>The solution is ( ____, _____ ).<\/p>\n<\/div><\/div>\n\n\n\n<p>The first equation is y=2x+3.<br>The y-intercept is 3. Plot the point (0,3).<br>The slope is 2. Move up 2 and right 1 to find another point on the line.<br>Draw a line connecting them.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-48.png\" alt=\"\" class=\"wp-image-11795\" style=\"width:518px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-48.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-48-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-48-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-48-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p>The second equation is y=x.<br>The y-intercept is 0. Plot the point (0,0).<br>The slope is 1. Move up 1 and right 1 to find another point on the line.<br>Draw a line connecting them.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-49.png\" alt=\"\" class=\"wp-image-11797\" style=\"width:450px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-49.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-49-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-49-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-49-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p>Finally, identify the point of intersection.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-51.png\" alt=\"\" class=\"wp-image-11798\" style=\"width:436px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-51.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-51-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-51-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-51-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p>The lines intersect at (\u20133,\u20133), so the solution to the simultaneous equations is (\u20133,\u20133).<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#9df2a3\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-be9c3c58c6ffd6bb0fbc9537f24f285f\" style=\"color:#b00012\">Solve these simultaneous equations by graphing. <\/p>\n\n\n\n<p>First graph the equations, and then type the solution.<br>y=2x\u20131<br>y=x+2<br>Click to select points on the graph.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-24-4.png\" alt=\"\" class=\"wp-image-11799\" style=\"width:458px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-24-4.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-24-4-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-24-4-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-24-4-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p>The solution is ( ____, _____ ).<\/p>\n<\/div><\/div>\n\n\n\n<p>The first equation is y=2x\u20131.<br>The y-intercept is\u20131Plot the point (0,\u20131).<br>The slope is 2. Move up 2 and right 1 to find another point on the line.<br>Draw a line connecting them.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-52.png\" alt=\"\" class=\"wp-image-11800\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-52.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-52-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-52-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-52-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p>The second equation is y=x+2.<br>The y-intercept is 2. Plot the point (0,2).<br>The slope is 1. Move up 1 and right 1 to find another point on the line.<br>Draw a line connecting them.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-53.png\" alt=\"\" class=\"wp-image-11805\" style=\"width:444px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-53.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-53-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-53-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-53-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p>Finally, identify the point of intersection.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-54.png\" alt=\"\" class=\"wp-image-11809\" style=\"width:480px;height:auto\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-54.png 1000w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-54-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-54-150x150.png 150w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-54-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p>The lines intersect at (3,5), so the solution to the simultaneous equations is (3,5).<\/p>\n<\/div><\/div>\n\n\n\n<h4 class=\"wp-block-heading has-text-color\" id=\"yui_3_18_1_1_1670028809318_7239\" style=\"color:#d90000\">Let&#8217;s practice:<\/h4>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 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-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/84022\/871\/787\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-27.png\" alt=\"\" class=\"wp-image-6703\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-27.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-27-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-27-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/85454\/686\/927\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-40.png\" alt=\"\" class=\"wp-image-6704\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-40.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-40-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-40-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Solve a pair of equations by graphing key notes: Solving&nbsp;systems&nbsp;of&nbsp;linear&nbsp; equations: You&nbsp;can solve systems of equations in a few different&nbsp;ways. Graphing: You&nbsp;can solve systems of equations by graphing. Look for the point where the lines&nbsp;intersect. Let&#8217;s&nbsp;try it! Solve the system of linear&nbsp;equations. Start&nbsp;by graphing the first equation,&nbsp;y=3x+7.&nbsp;Since this equation is in&nbsp;slope-intercept&nbsp;form,&nbsp;you can graph the line<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/e-2-solve-a-pair-of-equations-by-graphing\/\">Continue reading <span class=\"screen-reader-text\">&#8220;E.2 Solve a pair of equations by graphing&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-102","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/102","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=102"}],"version-history":[{"count":23,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/102\/revisions"}],"predecessor-version":[{"id":17603,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/102\/revisions\/17603"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=102"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}