{"id":100,"date":"2022-04-13T09:59:28","date_gmt":"2022-04-13T09:59:28","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=100"},"modified":"2025-01-22T09:36:53","modified_gmt":"2025-01-22T09:36:53","slug":"e-1-is-x-y-a-solution-to-the-pair-of-equations","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/e-1-is-x-y-a-solution-to-the-pair-of-equations\/","title":{"rendered":"E.1 Is (x, y) a solution to the pair of equations?"},"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>Is (x, y) a solution to the pair of equations?<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-04d9d6410ea0aa79bd5fd62d138d8458\" style=\"color:#74008b;text-transform:uppercase\">key notes:<\/p>\n\n\n\n<p class=\"has-large-font-size\">A point is a solution to simultaneous equations if plugging the point into each equation results in a true statement.<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-large-font-size\"><strong>Systems of equations&nbsp;:<\/strong><\/p>\n\n\n\n<p class=\"has-large-font-size\">A&nbsp;<strong>system<\/strong><strong>&nbsp;of&nbsp;<\/strong><strong>equations<\/strong>&nbsp;consists of two or more equations with the same variables. For example, the linear equations below create a system of linear&nbsp;equations:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li class=\"has-large-font-size\">y=2x\u20138<\/li>\n\n\n\n<li class=\"has-large-font-size\">3x\u20134y=7<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\">A&nbsp;<strong>solution<\/strong>&nbsp;to a system of equations is a set of values that makes each equation in the system true. The solution to the system of equations above can be written as the ordered pair&nbsp;(<strong>5<\/strong>,<strong>2<\/strong>)&nbsp;because&nbsp;x=5&nbsp;and&nbsp;y=2&nbsp;satisfy both equations in the system. To show this, you can substitute 5 for&nbsp;<em>x<\/em>&nbsp;and 2 for&nbsp;<em>y<\/em>&nbsp;into both&nbsp;equations.<\/p>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>y=2x\u20138<\/li>\n\n\n\n<li><strong>2<\/strong>=2(<strong>5<\/strong>)\u20138<\/li>\n\n\n\n<li>2=10\u20138<\/li>\n\n\n\n<li>2=2<\/li>\n<\/ul>\n\n\n\n<ul class=\"wp-block-list has-large-font-size\">\n<li>3x\u20134y=7<\/li>\n\n\n\n<li>3(<strong>5<\/strong>)\u20134(<strong>2<\/strong>)=7<\/li>\n\n\n\n<li>15\u20138=7<\/li>\n\n\n\n<li>7=7<\/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:#f1ec87\"><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-91829c713945dd2a7fb941f4915c061b\" style=\"color:#b00012\">Is&nbsp;(2,&nbsp;1)&nbsp;a solution to these simultaneous equations?<\/p>\n\n\n\n<p><em>x<\/em>&nbsp;+ 14<em>y<\/em>&nbsp;= 16<br>2<em>x<\/em>&nbsp;+ 5<em>y<\/em>&nbsp;= 9<\/p>\n<\/div><\/div>\n\n\n\n<p>In the ordered pair&nbsp;(2,&nbsp;1), 2 is the&nbsp;<em>x<\/em>-value&nbsp;and 1 is the&nbsp;<em>y<\/em>-value.<\/p>\n\n\n\n<p>In the first equation, replace&nbsp;<em>x<\/em>&nbsp;with 2 and&nbsp;<em>y<\/em>&nbsp;with 1.<\/p>\n\n\n\n<p>            <em>x<\/em>&nbsp;+ 14<em>y<\/em>&nbsp;=&nbsp;16<\/p>\n\n\n\n<p>         2 + 14(1) = 16<\/p>\n\n\n\n<p>              2+ 14 = 16<\/p>\n\n\n\n<p>                   16 = 16<\/p>\n\n\n\n<p>Yes, 16 = 16.<\/p>\n\n\n\n<p>Now in the second equation, replace&nbsp;<em>x<\/em>&nbsp;with 2 and&nbsp;<em>y<\/em>&nbsp;with 1.<\/p>\n\n\n\n<p>          2<em>x<\/em>&nbsp;+ 5<em>y<\/em>&nbsp;=&nbsp;9<br>     2(2)&nbsp;+ 5(1) = 9<\/p>\n\n\n\n<p>             4 + 5 = 9<\/p>\n\n\n\n<p>                   9 = 9<\/p>\n\n\n\n<p>Yes, 9 = 9.<\/p>\n\n\n\n<p>Plugging&nbsp;(2,&nbsp;1)&nbsp;into each equation resulted in a true statement. So,&nbsp;(2,&nbsp;1)&nbsp;is a solution to the simultaneous equations.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f6abab\"><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-baafd64e4565ddb538f3f1dbd7f96c6c\" style=\"color:#b00012\">Is (1, 1) a solution to these simultaneous equations?<\/p>\n\n\n\n<p>x + 4y = 14<br>2x + 18y = 20<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>In the ordered pair (1, 1), the x-value and the y-value are both 1.<\/p>\n\n\n\n<p>In the first equation, replace x and y with 1.<\/p>\n\n\n\n<p>x + 4y = 14<\/p>\n\n\n\n<p>1 + 4(1)?14<\/p>\n\n\n\n<p>1 + 4?14<\/p>\n\n\n\n<p>5?14<\/p>\n\n\n\n<p>No, 5 \u2260 14.<\/p>\n\n\n\n<p>Plugging (1, 1) into the first equation did not result in a true statement. So, (1, 1) is not a solution to the simultaneous equations.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#97f0f0\"><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-d76eb8e7faac8528627786ed0c72da97\" style=\"color:#b00012\">Is (3, 9) a solution to these simultaneous equations?<\/p>\n\n\n\n<p>y = 9x + 2<br>y = x + 6<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>yes<\/li>\n\n\n\n<li>no<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>In the ordered pair (3, 9), 3 is the x-value and 9 is the y-value.<\/p>\n\n\n\n<p>In the first equation, replace x with 3 and y with 9.<\/p>\n\n\n\n<p>y = 9x + 2<\/p>\n\n\n\n<p>9? 9(3) + 2<\/p>\n\n\n\n<p>9?27 + 2<\/p>\n\n\n\n<p>9?29<\/p>\n\n\n\n<p>No, 9 \u2260 29.<\/p>\n\n\n\n<p>Plugging (3, 9) into the first equation did not result in a true statement. So, (3, 9) is not a solution to the simultaneous equations.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s practise:<\/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\/84019\/363\/344\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-26.png\" alt=\"\" class=\"wp-image-6697\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-26.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-26-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-2-26-150x150.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\/85391\/566\/438\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-39.png\" alt=\"\" class=\"wp-image-6699\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-39.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-39-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-1-39-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Is (x, y) a solution to the pair of equations? key notes: A point is a solution to simultaneous equations if plugging the point into each equation results in a true statement. Systems of equations&nbsp;: A&nbsp;system&nbsp;of&nbsp;equations&nbsp;consists of two or more equations with the same variables. For example, the linear equations below create a system of<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/e-1-is-x-y-a-solution-to-the-pair-of-equations\/\">Continue reading <span class=\"screen-reader-text\">&#8220;E.1 Is (x, y) a solution to the pair of equations?&#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-100","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/100","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=100"}],"version-history":[{"count":19,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/100\/revisions"}],"predecessor-version":[{"id":17431,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/100\/revisions\/17431"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}