{"id":268194,"date":"2025-07-24T01:39:43","date_gmt":"2025-07-24T01:39:43","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=268194"},"modified":"2025-07-24T01:39:45","modified_gmt":"2025-07-24T01:39:45","slug":"find-3-solutions-ordered-pairs-for-the-equation-3x-2y-12","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/24\/find-3-solutions-ordered-pairs-for-the-equation-3x-2y-12\/","title":{"rendered":"Find 3 solutions (ordered pairs) for the equation 3x – 2y = 12"},"content":{"rendered":"\n

Find 3 solutions (ordered pairs) for the equation 3x – 2y = 12<\/p>\n\n\n\n

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

To find the solutions for the equation 3x\u22122y=123x – 2y = 123x\u22122y=12, we will solve for ordered pairs (x,y)(x, y)(x,y) by choosing different values for xxx and solving for yyy.<\/p>\n\n\n\n

Step-by-Step Process:<\/h3>\n\n\n\n
    \n
  1. Rewrite the equation for yyy:<\/strong> 3x\u22122y=12\u21d2\u22122y=12\u22123x\u21d2y=3x\u22121223x – 2y = 12 \\quad \\Rightarrow \\quad -2y = 12 – 3x \\quad \\Rightarrow \\quad y = \\frac{3x – 12}{2}3x\u22122y=12\u21d2\u22122y=12\u22123x\u21d2y=23x\u221212\u200b This equation tells us that for each value of xxx, we can substitute it in and solve for yyy.<\/li>\n<\/ol>\n\n\n\n

    Solution 1:<\/h3>\n\n\n\n

    Let x=0x = 0x=0:y=3(0)\u2212122=\u2212122=\u22126y = \\frac{3(0) – 12}{2} = \\frac{-12}{2} = -6y=23(0)\u221212\u200b=2\u221212\u200b=\u22126<\/p>\n\n\n\n

    Thus, one solution is (0,\u22126)(0, -6)(0,\u22126).<\/p>\n\n\n\n

    Solution 2:<\/h3>\n\n\n\n

    Let x=2x = 2x=2:y=3(2)\u2212122=6\u2212122=\u221262=\u22123y = \\frac{3(2) – 12}{2} = \\frac{6 – 12}{2} = \\frac{-6}{2} = -3y=23(2)\u221212\u200b=26\u221212\u200b=2\u22126\u200b=\u22123<\/p>\n\n\n\n

    Thus, the second solution is (2,\u22123)(2, -3)(2,\u22123).<\/p>\n\n\n\n

    Solution 3:<\/h3>\n\n\n\n

    Let x=4x = 4x=4:y=3(4)\u2212122=12\u2212122=02=0y = \\frac{3(4) – 12}{2} = \\frac{12 – 12}{2} = \\frac{0}{2} = 0y=23(4)\u221212\u200b=212\u221212\u200b=20\u200b=0<\/p>\n\n\n\n

    Thus, the third solution is (4,0)(4, 0)(4,0).<\/p>\n\n\n\n

    Summary of solutions:<\/h3>\n\n\n\n

    The three ordered pairs that satisfy the equation 3x\u22122y=123x – 2y = 123x\u22122y=12 are:<\/p>\n\n\n\n

      \n
    • (0,\u22126)(0, -6)(0,\u22126)<\/li>\n\n\n\n
    • (2,\u22123)(2, -3)(2,\u22123)<\/li>\n\n\n\n
    • (4,0)(4, 0)(4,0)<\/li>\n<\/ul>\n\n\n\n

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

      For each solution, we substituted a value of xxx into the equation and then calculated the corresponding value of yyy. The equation represents a linear relationship between xxx and yyy, and for any given value of xxx, we can find a corresponding yyy. These points lie on the line represented by the equation 3x\u22122y=123x – 2y = 123x\u22122y=12.<\/p>\n\n\n\n

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

      Find 3 solutions (ordered pairs) for the equation 3x – 2y = 12 The Correct Answer and Explanation is: To find the solutions for the equation 3x\u22122y=123x – 2y = 123x\u22122y=12, we will solve for ordered pairs (x,y)(x, y)(x,y) by choosing different values for xxx and solving for yyy. Step-by-Step Process: Solution 1: Let x=0x […]<\/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-268194","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/268194","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=268194"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/268194\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=268194"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=268194"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=268194"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}