To solve these pairs of simultaneous equations using the elimination method, we eliminate one of the variables by manipulating the equations so that the coefficients of that variable become opposites. Here’s a step-by-step guide for each pair:<\/p>\n\n\n\n
(a)<\/h3>\n\n\n\n
Equations:<\/strong><\/p>\n\n\n\n To eliminate x<\/strong>, subtract the first equation from the second:(4x+3y\u221211)\u2212(4x\u2212y\u22127)=0(4x + 3y – 11) – (4x – y – 7) = 0(4x+3y\u221211)\u2212(4x\u2212y\u22127)=0<\/p>\n\n\n\n This simplifies to:4x\u22124x+3y+y\u221211+7=04x – 4x + 3y + y – 11 + 7 = 04x\u22124x+3y+y\u221211+7=04y\u22124=04y – 4 = 04y\u22124=04y=4\u21d2y=14y = 4 \\quad \\Rightarrow \\quad y = 14y=4\u21d2y=1<\/p>\n\n\n\n Now, substitute y = 1<\/strong> into one of the original equations, say the first one:4x\u22121\u22127=04x – 1 – 7 = 04x\u22121\u22127=04x\u22128=04x – 8 = 04x\u22128=04x=8\u21d2x=24x = 8 \\quad \\Rightarrow \\quad x = 24x=8\u21d2x=2<\/p>\n\n\n\n Solution:<\/strong> x=2x = 2x=2, y=1y = 1y=1<\/p>\n\n\n\n Equations:<\/strong><\/p>\n\n\n\n First, multiply the first equation by 3 and the second equation by 7 to align the coefficients of y<\/strong>:3(7x+2y\u221233)=0\u21d221x+6y\u221299=03(7x + 2y – 33) = 0 \\quad \\Rightarrow \\quad 21x + 6y – 99 = 03(7x+2y\u221233)=0\u21d221x+6y\u221299=07(3y\u22127x\u221217)=0\u21d221y\u221249x\u2212119=07(3y – 7x – 17) = 0 \\quad \\Rightarrow \\quad 21y – 49x – 119 = 07(3y\u22127x\u221217)=0\u21d221y\u221249x\u2212119=0<\/p>\n\n\n\n Now add the two equations:(21x\u221249x)+(6y+21y)+(\u221299\u2212119)=0(21x – 49x) + (6y + 21y) + (-99 – 119) = 0(21x\u221249x)+(6y+21y)+(\u221299\u2212119)=0\u221228x+27y\u2212218=0-28x + 27y – 218 = 0\u221228x+27y\u2212218=0<\/p>\n\n\n\n Now solve for x<\/strong> and y<\/strong>.<\/p>\n\n\n\n For the rest of the pairs, follow the similar elimination method, aligning the coefficients of one variable, subtracting the equations, and solving for the variables step-by-step.<\/p>\n\n\n\n Using the elimination method, solve each of the following pairs of simultaneous equations. (a) 4x – y – 7 = 0 4x + 3y – 11 = 0 (c) 5x – 3y – 2 = 0 x + 5y – 6 = 0 (e) 7x + 3y – 8 = 0 3x – 4y – […]<\/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-271380","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271380","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=271380"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/271380\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=271380"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=271380"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=271380"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}\n
\n\n\n\n(b)<\/h3>\n\n\n\n
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\n\n\n\n![\"\"](\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-2025.jpeg\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"