{"id":11155,"date":"2022-06-22T20:05:38","date_gmt":"2022-06-22T14:35:38","guid":{"rendered":"https:\/\/mathemerize.com\/?p=11155"},"modified":"2022-06-22T20:05:42","modified_gmt":"2022-06-22T14:35:42","slug":"solve-the-following-pair-of-linear-equations-by-the-substitution-and-cross-multiplication-methods-8x-5y-9-and-3x-2y-4","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/solve-the-following-pair-of-linear-equations-by-the-substitution-and-cross-multiplication-methods-8x-5y-9-and-3x-2y-4\/","title":{"rendered":"Solve the following pair of linear equations by the substitution and cross-multiplication methods : 8x + 5y = 9 and 3x + 2y = 4"},"content":{"rendered":"

Solution :<\/h2>\n

The given linear equations are :<\/p>\n

8x + 5y = 9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ………..(1)<\/p>\n

3x + 2y = 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ………..(2)<\/p>\n

By Substitution Method :<\/strong><\/p>\n

Form equation (1),\u00a0 y = \\(9 – 8x\\over 5\\)<\/p>\n

Substitute the value of y in equation (2), we get<\/p>\n

3x + 2(\\(9 – 8x\\over 5\\)) = 4<\/p>\n

or\u00a0 \u00a015x + 18 – 16x = 20\u00a0 \u00a0 \u00a0\\(\\implies\\)\u00a0 \u00a0x = -2<\/p>\n

Putting x = – 2 in equation (1), we get<\/p>\n

8(-2) + 5y = 9\u00a0 \u00a0 \\(\\implies\\)\u00a0 \u00a05y = 9 + 16 = 25<\/p>\n

\\(\\implies\\)\u00a0 y = 5<\/p>\n

Hence,\u00a0 x = -2 and y = 5.<\/strong><\/p>\n

By Cross-Multiplication Method :<\/strong><\/p>\n

The given linear equation can be written as :<\/p>\n

8x + 5y – 9 = 0<\/p>\n

3x + 2y – 4 = 0<\/p>\n

So, we have<\/p>\n

\\(x\\over -20 + 18\\)\u00a0 =\u00a0 \\(y\\over -27 + 32\\)\u00a0 =\u00a0 \\(1\\over 16 – 15\\)<\/p>\n

\\(\\implies\\)\u00a0 \u00a0\\(x\\over -2\\)\u00a0 =\u00a0 \\(y\\over\u00a0 5\\)\u00a0 =\u00a0 \\(1\\over 1\\)<\/p>\n

\\(\\implies\\)\u00a0 \u00a0x = -2\u00a0 and y = 5<\/strong><\/p>\n\n\n

<\/p>\n\n\n\n

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

Solution : The given linear equations are : 8x + 5y = 9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ………..(1) 3x + 2y = 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ………..(2) By Substitution Method : Form equation (1),\u00a0 y = \\(9 – 8x\\over 5\\) Substitute the value of y in equation (2), we get …<\/p>\n

Solve the following pair of linear equations by the substitution and cross-multiplication methods : 8x + 5y = 9 and 3x + 2y = 4<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[911,43],"tags":[],"yoast_head":"\nSolve the following pair of linear equations by the substitution and cross-multiplication methods : 8x + 5y = 9 and 3x + 2y = 4 - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/solve-the-following-pair-of-linear-equations-by-the-substitution-and-cross-multiplication-methods-8x-5y-9-and-3x-2y-4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Solve the following pair of linear equations by the substitution and cross-multiplication methods : 8x + 5y = 9 and 3x + 2y = 4 - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : The given linear equations are : 8x + 5y = 9\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ………..(1) 3x + 2y = 4\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 ………..(2) By Substitution Method : Form equation (1),\u00a0 y = (9 – 8xover 5) Substitute the value of y in equation (2), we get … Solve the following pair of linear equations by the substitution and cross-multiplication methods : 8x + 5y = 9 and 3x + 2y = 4 Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/solve-the-following-pair-of-linear-equations-by-the-substitution-and-cross-multiplication-methods-8x-5y-9-and-3x-2y-4\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2022-06-22T14:35:38+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-06-22T14:35:42+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/solve-the-following-pair-of-linear-equations-by-the-substitution-and-cross-multiplication-methods-8x-5y-9-and-3x-2y-4\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/solve-the-following-pair-of-linear-equations-by-the-substitution-and-cross-multiplication-methods-8x-5y-9-and-3x-2y-4\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Solve the following pair of linear equations by the substitution and cross-multiplication methods : 8x + 5y = 9 and 3x + 2y = 4\",\"datePublished\":\"2022-06-22T14:35:38+00:00\",\"dateModified\":\"2022-06-22T14:35:42+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/solve-the-following-pair-of-linear-equations-by-the-substitution-and-cross-multiplication-methods-8x-5y-9-and-3x-2y-4\/\"},\"wordCount\":115,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Linear Equation in Two Variables Questions\",\"Maths Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/solve-the-following-pair-of-linear-equations-by-the-substitution-and-cross-multiplication-methods-8x-5y-9-and-3x-2y-4\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/solve-the-following-pair-of-linear-equations-by-the-substitution-and-cross-multiplication-methods-8x-5y-9-and-3x-2y-4\/\",\"url\":\"https:\/\/mathemerize.com\/solve-the-following-pair-of-linear-equations-by-the-substitution-and-cross-multiplication-methods-8x-5y-9-and-3x-2y-4\/\",\"name\":\"Solve the following pair of linear equations by the substitution and cross-multiplication methods : 8x + 5y = 9 and 3x + 2y = 4 - 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