{"id":114,"date":"2022-04-13T10:02:04","date_gmt":"2022-04-13T10:02:04","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=114"},"modified":"2024-12-20T08:31:05","modified_gmt":"2024-12-20T08:31:05","slug":"e-8-solve-a-pair-of-equations-using-elimination","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/e-8-solve-a-pair-of-equations-using-elimination\/","title":{"rendered":"E.8 Solve a pair of equations using elimination"},"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 using elimination<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-ac2bc047fac346cd34a46d2a76287634\" style=\"color:#74008b;text-transform:capitalize\">key notes:<\/p>\n\n\n\n<p class=\"has-large-font-size\">To solve using elimination, follow these four steps:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">Step 1: Make sure the equations have opposite&nbsp;<em>x<\/em>&nbsp;terms or opposite&nbsp;<em>y<\/em>&nbsp;terms.<\/li>\n\n\n\n<li class=\"has-large-font-size\">Step 2: Add to eliminate one variable and solve for the other.<\/li>\n\n\n\n<li class=\"has-large-font-size\">Step 3: Plug the result of Step 2 into one of the original equations and solve.<\/li>\n\n\n\n<li class=\"has-large-font-size\">Step 4: State the solution.<\/li>\n<\/ul>\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:#d6f9f1\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-70e588cd146a03f7d5c95179c39f4dee\" style=\"color:#b00012\">Solve using elimination.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>8<em>x<\/em>&nbsp;+ 2<em>y<\/em>&nbsp;=&nbsp;-16<\/li>\n\n\n\n<li>8<em>x<\/em>&nbsp;\u2212 6<em>y<\/em>&nbsp;= 16<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Use elimination to solve the simultaneous equations:<\/p>\n\n\n\n<p>8x + 2y = \u201316<br>8x \u2212 6y = 16<\/p>\n\n\n\n<p>Step 1: Make sure the equations have opposite x terms or opposite y terms.<\/p>\n\n\n\n<p>Currently, neither the x terms (8x and 8x) nor the y terms (2y and \u20136y) are opposites. Use multiplication to rewrite the equations with either opposite x terms or opposite y terms. One good approach is to multiply the first equation by \u20131.<\/p>\n\n\n\n<p>\u2013(8x + 2y = \u201316)  \u2192   \u20138x \u2212 2y = 16<br><br>8x + \u20136y = 16      \u2192   8x \u2212 6y = 16<\/p>\n\n\n\n<p><br>Now the x terms (\u20138x and 8x) are opposites.<\/p>\n\n\n\n<p>Step 2: Add to eliminate one variable and solve for the other.<\/p>\n\n\n\n<p>Add to eliminate the x terms, and then solve for y.<\/p>\n\n\n\n<p style=\"line-height:0\">      \u20138x \u2212 2y = 16<\/p>\n\n\n\n<p style=\"line-height:0\">+    <span style=\"text-decoration: underline;\">( 8x \u2212 6y = 16 )<\/span><\/p>\n\n\n\n<p style=\"line-height:0\"><br>         0x \u2212 8y = 32          &#8212;&gt; Add to eliminate the x terms<\/p>\n\n\n\n<p>\u20138y = 32            &#8212;-&gt; Simplify<\/p>\n\n\n\n<p>y = \u20134             &#8212;&#8212;&gt; Divide both sides by \u20138<\/p>\n\n\n\n<p><strong>Step 3: Plug the result of Step 2 into one of the original equations and solve.<\/strong><\/p>\n\n\n\n<p>Take the result of Step 2,&nbsp;<em>y<\/em>&nbsp;=&nbsp;-4, and plug it into one of the original equations, such as&nbsp;8<em>x<\/em>&nbsp;+ 2<em>y<\/em>&nbsp;=&nbsp;-16. Then find the value of&nbsp;<em>x<\/em>.<\/p>\n\n\n\n<p>8<em>x<\/em>&nbsp;+ 2<strong><em>y<\/em><\/strong>&nbsp;=&nbsp;-16<br>8x&nbsp;+ 2(<strong>-4<\/strong>)&nbsp;=&nbsp;-16   &#8212;&gt;Plug in&nbsp;y&nbsp;=&nbsp;-4<br>8x&nbsp;\u2212 8&nbsp;=&nbsp;-16     &#8212;&#8212;&gt;Multiply<br>8x&nbsp;=&nbsp;-8     &#8212;&#8211;&gt;Add 8 to both sides<br>x&nbsp;=&nbsp;-1      &#8212;-&gt;Divide both sides by 8<\/p>\n\n\n\n<p><strong>Step 4: State the solution.<\/strong><\/p>\n\n\n\n<p>Since&nbsp;<em>x<\/em>&nbsp;=&nbsp;-1 and&nbsp;<em>y<\/em>&nbsp;=&nbsp;-4, the solution is&nbsp;(-1,&nbsp;-4).<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#dac4f5\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-70e588cd146a03f7d5c95179c39f4dee\" style=\"color:#b00012\">Solve using elimination.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>x<\/em>&nbsp;\u2212 2<em>y<\/em>&nbsp;=&nbsp;-9<\/li>\n\n\n\n<li><em>x<\/em>&nbsp;\u2212 3<em>y<\/em>&nbsp;=&nbsp;-16<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Use elimination to solve the simultaneous equations:<\/p>\n\n\n\n<p><em>x<\/em>&nbsp;\u2212 2<em>y<\/em>&nbsp;=&nbsp;-9<em>x<\/em>&nbsp;\u2212 3<em>y<\/em>&nbsp;=&nbsp;-16<\/p>\n\n\n\n<p><strong>Step 1: Make sure the equations have opposite&nbsp;<em>x<\/em>&nbsp;terms or opposite&nbsp;<em>y<\/em>&nbsp;terms.<\/strong><\/p>\n\n\n\n<p>Currently, neither the&nbsp;<em>x<\/em>&nbsp;terms (<em>x<\/em>&nbsp;and&nbsp;<em>x<\/em>) nor the&nbsp;<em>y<\/em>&nbsp;terms (-2<em>y<\/em>&nbsp;and&nbsp;-3<em>y<\/em>) are opposites. Use multiplication to rewrite the equations with either opposite&nbsp;<em>x<\/em>&nbsp;terms or opposite&nbsp;<em>y<\/em>&nbsp;terms. One good approach is to multiply the first equation by&nbsp;-1.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>-(<em>x<\/em>&nbsp;\u2212 2<em>y<\/em>&nbsp;=&nbsp;-9)<\/td><td>&nbsp;\u2192&nbsp;<\/td><td><em>-x<\/em>&nbsp;+&nbsp;<strong>2<\/strong><em>y<\/em>&nbsp;=&nbsp;<strong>9<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td><em>x<\/em>&nbsp;+&nbsp;-3<em>y<\/em>&nbsp;=&nbsp;-16<\/td><td>&nbsp;\u2192&nbsp;<\/td><td><em>x<\/em>&nbsp;\u2212 3<em>y<\/em>&nbsp;=&nbsp;-16<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Now the&nbsp;<em>x<\/em>&nbsp;terms (<em>-x<\/em>&nbsp;and&nbsp;<em>x<\/em>) are opposites.<\/p>\n\n\n\n<p><strong>Step 2: Add to eliminate one variable and solve for the other.<\/strong><\/p>\n\n\n\n<p>Add to eliminate the&nbsp;<em>x<\/em>&nbsp;terms, and then solve for&nbsp;<em>y<\/em>.<\/p>\n\n\n\n<p style=\"line-height:0\">      \u2013x + 2y = 9<\/p>\n\n\n\n<p style=\"line-height:0\">+   <span style=\"text-decoration: underline;\">( x \u2212 3y = \u201316 )<\/span><\/p>\n\n\n\n<p style=\"line-height:0\">          x \u2212 y = \u20137             &#8212;&#8211;&gt;Add to eliminate the x terms<\/p>\n\n\n\n<p>    \u2013y = \u20137 Simplify<\/p>\n\n\n\n<p>      y = 7 Multiply both sides by \u20131<\/p>\n\n\n\n<p><strong>Step 3: Plug the result of Step 2 into one of the original equations and solve.<\/strong><\/p>\n\n\n\n<p>Take the result of Step 2,&nbsp;<em>y<\/em>&nbsp;= 7, and plug it into one of the original equations, such as&nbsp;<em>x<\/em>&nbsp;+&nbsp;-2<em>y<\/em>&nbsp;=&nbsp;-9. Then find the value of&nbsp;<em>x<\/em>.<\/p>\n\n\n\n<p><em>x<\/em>&nbsp;\u2212 2<strong><em>y<\/em><\/strong>&nbsp;=&nbsp;-9<br><em>x<\/em>&nbsp;\u2212 2(<strong>7<\/strong>)&nbsp;=&nbsp;-9     &#8212;&gt;Plug in&nbsp;y&nbsp;= 7<br><em>x<\/em>&nbsp;\u2212 14&nbsp;=&nbsp;-9      &#8212;&gt;Multiply<br><em>x<\/em>&nbsp;=&nbsp;5        &#8212;&gt;Add 14 to both sides<\/p>\n\n\n\n<p><strong>Step 4: State the solution.<\/strong><\/p>\n\n\n\n<p>Since&nbsp;<em>x<\/em>&nbsp;= 5 and&nbsp;<em>y<\/em>&nbsp;= 7, the solution is&nbsp;(5,&nbsp;7).<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f3b3b3\"><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-704a5cefe79c86a753515cc39c96d803\" style=\"color:#b00012\">Solve using elimination. <\/p>\n\n\n\n<p>-6x &#8211; 5y = -15<\/p>\n\n\n\n<p>6x + 9y = 3<\/p>\n\n\n\n<p>( ______ , ______ )<\/p>\n<\/div><\/div>\n\n\n\n<p>Use elimination to solve the simultaneous equations:<\/p>\n\n\n\n<p>\u20136x \u2212 5y = \u201315<br>6x + 9y = 3<\/p>\n\n\n\n<p>Step 1: Make sure the equations have opposite x terms or opposite y terms.<\/p>\n\n\n\n<p>The x terms (\u20136x and 6x) are already opposites.<\/p>\n\n\n\n<p>Step 2: Add to eliminate one variable and solve for the other.<\/p>\n\n\n\n<p>Add to eliminate the x terms, and then solve for y.<\/p>\n\n\n\n<p>\u20136x \u2212 5y = \u201315<\/p>\n\n\n\n<p><span style=\"text-decoration: underline;\">+( 6x + 9y = 3 )<\/span><br>0x + 4y = \u201312           Add to eliminate the x terms<\/p>\n\n\n\n<p>4y = \u201312 Simplify<\/p>\n\n\n\n<p>y = \u20133 Divide both sides by 4<\/p>\n\n\n\n<p>Step 3: Plug the result of Step 2 into one of the original equations and solve.<\/p>\n\n\n\n<p>Take the result of Step 2, y = \u20133, and plug it into one of the original equations, such as \u20136x + \u20135y = \u201315. Then find the value of x.<\/p>\n\n\n\n<p>\u20136x \u2212 5y = \u201315<\/p>\n\n\n\n<p>\u20136x \u2212 5(\u20133) = \u201315 Plugin y = \u20133<\/p>\n\n\n\n<p>\u20136x + 15 = \u201315 Multiply<\/p>\n\n\n\n<p>\u20136x = \u201330 Subtract 15 from both sides<\/p>\n\n\n\n<p>x = 5 Divide both sides by \u20136<\/p>\n\n\n\n<p>Step 4: State the solution.<\/p>\n\n\n\n<p>Since x = 5 and y = \u20133, the solution is (5, \u20133).<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-e9969cedcddfdc22a0f1cf481aeb5cd5\" style=\"color:#d90000\">Let&#8217;s practice:<\/p>\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\/84108\/429\/445\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-22.png\" alt=\"\" class=\"wp-image-6656\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-22.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-22-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-22-150x150.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\/37824\/873\/181\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-33.png\" alt=\"\" class=\"wp-image-6657\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-33.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-33-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-33-150x150.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 using elimination key notes: To solve using elimination, follow these four steps: Learn with an example Solve using elimination. Use elimination to solve the simultaneous equations: 8x + 2y = \u2013168x \u2212 6y = 16 Step 1: Make sure the equations have opposite x terms or opposite y terms. Currently,<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/e-8-solve-a-pair-of-equations-using-elimination\/\">Continue reading <span class=\"screen-reader-text\">&#8220;E.8 Solve a pair of equations using elimination&#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-114","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/114","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=114"}],"version-history":[{"count":28,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/114\/revisions"}],"predecessor-version":[{"id":15445,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/114\/revisions\/15445"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}