{"id":167351,"date":"2024-11-15T16:21:43","date_gmt":"2024-11-15T16:21:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=167351"},"modified":"2024-11-15T16:21:45","modified_gmt":"2024-11-15T16:21:45","slug":"solve-the-following-system-x-2-y-3-x-y-3","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/15\/solve-the-following-system-x-2-y-3-x-y-3\/","title":{"rendered":"Solve the following system. x 2 &#8211; y = 3 x &#8211; y = -3"},"content":{"rendered":"\n<p>Solve the following system. x 2 &#8211; y = 3 x &#8211; y = -3 The solution set<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>We are given the system of equations:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>( x^2 &#8211; y = 3 )<\/li>\n\n\n\n<li>( x &#8211; y = -3 )<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Solve for ( y ) in the second equation<\/h3>\n\n\n\n<p>From the second equation, ( x &#8211; y = -3 ), we can isolate ( y ) as follows:<\/p>\n\n\n\n<p>[<br>x &#8211; y = -3<br>]<br>[<br>y = x + 3<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Substitute the expression for ( y ) into the first equation<\/h3>\n\n\n\n<p>Now that we have ( y = x + 3 ), substitute this into the first equation ( x^2 &#8211; y = 3 ):<\/p>\n\n\n\n<p>[<br>x^2 &#8211; (x + 3) = 3<br>]<\/p>\n\n\n\n<p>Simplify the equation:<\/p>\n\n\n\n<p>[<br>x^2 &#8211; x &#8211; 3 = 3<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Solve the resulting quadratic equation<\/h3>\n\n\n\n<p>To solve for ( x ), first move all terms to one side:<\/p>\n\n\n\n<p>[<br>x^2 &#8211; x &#8211; 3 &#8211; 3 = 0<br>]<br>[<br>x^2 &#8211; x &#8211; 6 = 0<br>]<\/p>\n\n\n\n<p>Now factor the quadratic equation:<\/p>\n\n\n\n<p>[<br>x^2 &#8211; x &#8211; 6 = (x &#8211; 3)(x + 2) = 0<br>]<\/p>\n\n\n\n<p>Set each factor equal to zero:<\/p>\n\n\n\n<p>[<br>x &#8211; 3 = 0 \\quad \\text{or} \\quad x + 2 = 0<br>]<\/p>\n\n\n\n<p>Solving these gives:<\/p>\n\n\n\n<p>[<br>x = 3 \\quad \\text{or} \\quad x = -2<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Find the corresponding values of ( y )<\/h3>\n\n\n\n<p>We now substitute these values of ( x ) into the equation ( y = x + 3 ) to find the corresponding values of ( y ):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If ( x = 3 ), then ( y = 3 + 3 = 6 ).<\/li>\n\n\n\n<li>If ( x = -2 ), then ( y = -2 + 3 = 1 ).<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 5: Conclusion<\/h3>\n\n\n\n<p>The solution set is ( (3, 6) ) and ( (-2, 1) ).<\/p>\n\n\n\n<p>Thus, the solutions to the system are ( \\boxed{(3, 6) \\text{ and } (-2, 1)} ).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>We started by isolating one variable, ( y ), from the second equation. We substituted this expression into the first equation, resulting in a quadratic equation. After solving the quadratic, we found two possible values for ( x ) and then substituted those into the equation for ( y ) to find the corresponding values. This approach ensures that both equations are satisfied by the solutions we found.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solve the following system. x 2 &#8211; y = 3 x &#8211; y = -3 The solution set The Correct Answer and Explanation is: We are given the system of equations: Step 1: Solve for ( y ) in the second equation From the second equation, ( x &#8211; y = -3 ), we can [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-167351","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167351","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=167351"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/167351\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=167351"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=167351"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=167351"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}