{"id":261214,"date":"2025-07-19T21:51:10","date_gmt":"2025-07-19T21:51:10","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=261214"},"modified":"2025-07-19T21:51:12","modified_gmt":"2025-07-19T21:51:12","slug":"4x-3y-6-4x-2y-14-solve-the-system-of-equations","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/19\/4x-3y-6-4x-2y-14-solve-the-system-of-equations\/","title":{"rendered":"4x + 3y = 6 -4x + 2y = 14 Solve the system of equations."},"content":{"rendered":"\n

4x + 3y = 6 -4x + 2y = 14 Solve the system of equations.<\/p>\n\n\n\n

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

We have the following system of equations:<\/p>\n\n\n\n

    \n
  1. 4x+3y=64x + 3y = 64x+3y=6<\/li>\n\n\n\n
  2. \u22124x+2y=14-4x + 2y = 14\u22124x+2y=14<\/li>\n<\/ol>\n\n\n\n

    We will solve this system using the elimination method<\/strong>. The idea is to manipulate the equations such that one of the variables cancels out when the equations are added or subtracted.<\/p>\n\n\n\n

    Step 1: Eliminate one variable<\/h3>\n\n\n\n

    Looking at the two equations, notice that the coefficients of xxx in both equations are opposites (4 and -4). We can eliminate xxx by adding both equations.<\/p>\n\n\n\n

    Adding the two equations:<\/h4>\n\n\n\n

    (4x+3y)+(\u22124x+2y)=6+14(4x + 3y) + (-4x + 2y) = 6 + 14(4x+3y)+(\u22124x+2y)=6+14<\/p>\n\n\n\n

    This simplifies to:(4x\u22124x)+(3y+2y)=20(4x – 4x) + (3y + 2y) = 20(4x\u22124x)+(3y+2y)=200x+5y=200x + 5y = 200x+5y=20<\/p>\n\n\n\n

    Now we have:5y=205y = 205y=20<\/p>\n\n\n\n

    Step 2: Solve for yyy<\/h3>\n\n\n\n

    To solve for yyy, divide both sides of the equation by 5:y=205=4y = \\frac{20}{5} = 4y=520\u200b=4<\/p>\n\n\n\n

    Step 3: Substitute y=4y = 4y=4 into one of the original equations<\/h3>\n\n\n\n

    Now that we know y=4y = 4y=4, we can substitute this value back into one of the original equations to solve for xxx. Let’s use the first equation:4x+3y=64x + 3y = 64x+3y=6<\/p>\n\n\n\n

    Substitute y=4y = 4y=4 into this equation:4x+3(4)=64x + 3(4) = 64x+3(4)=64x+12=64x + 12 = 64x+12=6<\/p>\n\n\n\n

    Now, subtract 12 from both sides:4x=6\u2212124x = 6 – 124x=6\u2212124x=\u221264x = -64x=\u22126<\/p>\n\n\n\n

    Divide by 4:x=\u221264=\u221232x = \\frac{-6}{4} = -\\frac{3}{2}x=4\u22126\u200b=\u221223\u200b<\/p>\n\n\n\n

    Final Solution:<\/h3>\n\n\n\n

    The solution to the system of equations is:x=\u221232,y=4x = -\\frac{3}{2}, \\quad y = 4x=\u221223\u200b,y=4<\/p>\n\n\n\n

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

    We used the elimination method to eliminate xxx and solve for yyy. Then, we substituted y=4y = 4y=4 into one of the original equations to find x=\u221232x = -\\frac{3}{2}x=\u221223\u200b. The solution is (\u221232,4)\\left( -\\frac{3}{2}, 4 \\right)(\u221223\u200b,4).<\/p>\n\n\n\n

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

    4x + 3y = 6 -4x + 2y = 14 Solve the system of equations. The Correct Answer and Explanation is: We have the following system of equations: We will solve this system using the elimination method. The idea is to manipulate the equations such that one of the variables cancels out when the equations […]<\/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-261214","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261214","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=261214"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/261214\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=261214"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=261214"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=261214"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}