{"id":164254,"date":"2024-11-10T06:14:16","date_gmt":"2024-11-10T06:14:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=164254"},"modified":"2024-11-10T06:14:18","modified_gmt":"2024-11-10T06:14:18","slug":"solve-the-formula-axbyc-for-y","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/10\/solve-the-formula-axbyc-for-y\/","title":{"rendered":"Solve the formula Ax+By=C for y"},"content":{"rendered":"\n

Solve the formula Ax+By=C for y.<\/p>\n\n\n\n

A. y = C\/B + Ax O<\/p>\n\n\n\n

B. y = (C – Ax)\/B <\/p>\n\n\n\n

C. y = (C + Ax)\/B <\/p>\n\n\n\n

D. y = C – (Ax)\/B<\/p>\n\n\n\n

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

The correct answer is B.<\/strong> ( y = \\frac{C – Ax}{B} ).<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To solve for ( y ) in the equation ( Ax + By = C ), you need to isolate ( y ) on one side of the equation.<\/p>\n\n\n\n

Step-by-Step Solution:<\/h4>\n\n\n\n
    \n
  1. Start with the original equation:<\/strong>
    [
    Ax + By = C
    ]<\/li>\n\n\n\n
  2. Subtract ( Ax ) from both sides<\/strong> to move the term involving ( x ) to the right side:
    [
    By = C – Ax
    ]<\/li>\n\n\n\n
  3. Divide both sides by ( B )<\/strong> to solve for ( y ):
    [
    y = \\frac{C – Ax}{B}
    ]<\/li>\n<\/ol>\n\n\n\n

    Thus, the solution is ( y = \\frac{C – Ax}{B} ), which matches option B<\/strong>.<\/p>\n\n\n\n

    Why This Solution Works<\/h3>\n\n\n\n

    In algebra, isolating a variable requires performing inverse operations to “undo” the terms around the variable you\u2019re solving for. In this case, we\u2019re solving for ( y ), so we need to remove any terms attached to it. Starting with ( Ax ) and ( By = C ), we remove ( Ax ) first by moving it to the other side of the equation. Finally, since ( y ) is multiplied by ( B ), we divide both sides by ( B ) to get ( y ) by itself.<\/p>\n\n\n\n

    Common Mistakes and Why Other Options are Incorrect<\/h3>\n\n\n\n
      \n
    1. Option A<\/strong>: ( y = \\frac{C}{B} + Ax )<\/li>\n<\/ol>\n\n\n\n
        \n
      • This mistakenly places ( Ax ) on the right side without subtraction, which doesn\u2019t align with the original equation.<\/li>\n<\/ul>\n\n\n\n
          \n
        1. Option C<\/strong>: ( y = \\frac{C + Ax}{B} )<\/li>\n<\/ol>\n\n\n\n
            \n
          • This incorrectly suggests adding ( Ax ) to ( C ) instead of subtracting it, which changes the original equation\u2019s meaning.<\/li>\n<\/ul>\n\n\n\n
              \n
            1. Option D<\/strong>: ( y = C – \\frac{Ax}{B} )<\/li>\n<\/ol>\n\n\n\n
                \n
              • Here, only ( Ax ) is divided by ( B ), while ( C ) is not, which isn\u2019t correct given the algebraic manipulation needed.<\/li>\n<\/ul>\n\n\n\n

                This approach ensures accuracy and is foundational for manipulating equations in algebra.<\/p>\n","protected":false},"excerpt":{"rendered":"

                Solve the formula Ax+By=C for y. A. y = C\/B + Ax O B. y = (C – Ax)\/B C. y = (C + Ax)\/B D. y = C – (Ax)\/B The Correct Answer and Explanation is : The correct answer is B. ( y = \\frac{C – Ax}{B} ). Explanation: To solve for ( […]<\/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-164254","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164254","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=164254"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/164254\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=164254"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=164254"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=164254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}