{"id":246065,"date":"2025-07-06T18:08:43","date_gmt":"2025-07-06T18:08:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=246065"},"modified":"2025-07-06T18:08:45","modified_gmt":"2025-07-06T18:08:45","slug":"use-substitution-to-solve-the-system","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/use-substitution-to-solve-the-system\/","title":{"rendered":"Use substitution to solve the system"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

The correct choice is:
A. The solution is (0, -5).<\/strong><\/p>\n\n\n\n

To solve the system of equations using the substitution method, we first need to isolate one variable in one of the equations. The given system is:<\/p>\n\n\n\n

    \n
  1. 2x + 9y = -45<\/li>\n\n\n\n
  2. 5x – y = 5<\/li>\n<\/ol>\n\n\n\n

    The second equation, 5x – y = 5, is the easiest to rearrange to solve for one variable. We can isolate y by first subtracting 5x from both sides, which gives us -y = 5 – 5x. Then, by multiplying the entire equation by -1, we get y = -5 + 5x, or more simply, y = 5x – 5.<\/p>\n\n\n\n

    Now that we have an expression for y, we substitute it into the first equation, 2x + 9y = -45. This step replaces the y variable in the first equation with our new expression involving x. The substitution results in the following equation with only one variable, x:
    2x + 9(5x – 5) = -45<\/p>\n\n\n\n

    Next, we solve this equation for x. We start by distributing the 9 into the parentheses:
    2x + 45x – 45 = -45<\/p>\n\n\n\n

    Combine the x terms on the left side:
    47x – 45 = -45<\/p>\n\n\n\n

    To isolate the term with x, we add 45 to both sides of the equation:
    47x = 0<\/p>\n\n\n\n

    Finally, we divide both sides by 47 to find the value of x:
    x = 0<\/p>\n\n\n\n

    With the value of x found, we can now find the value of y. We substitute x = 0 back into the equation we derived earlier, y = 5x – 5:
    y = 5(0) – 5
    y = 0 – 5
    y = -5<\/p>\n\n\n\n

    The solution to the system is the ordered pair (x, y), which is (0, -5). We can verify this solution by plugging these values back into both original equations to ensure they hold true.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    The Correct Answer and Explanation is: The correct choice is:A. The solution is (0, -5). To solve the system of equations using the substitution method, we first need to isolate one variable in one of the equations. The given system is: The second equation, 5x – y = 5, is the easiest to rearrange to solve […]<\/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-246065","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246065","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=246065"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246065\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=246065"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=246065"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=246065"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}