{"id":265609,"date":"2025-07-22T07:49:23","date_gmt":"2025-07-22T07:49:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=265609"},"modified":"2025-07-22T07:49:26","modified_gmt":"2025-07-22T07:49:26","slug":"which-ordered-pair-makes-both-inequalities-true-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/22\/which-ordered-pair-makes-both-inequalities-true-2\/","title":{"rendered":"Which ordered pair makes both inequalities true"},"content":{"rendered":"\n

Which ordered pair makes both inequalities true? y > -3x + 3 y ? 2x – 2 (1,0) (-1,1) (2,2)<\/p>\n\n\n\n

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

We are given two inequalities:<\/p>\n\n\n\n

    \n
  1. y>\u22123x+3y > -3x + 3y>\u22123x+3<\/li>\n\n\n\n
  2. y\u22642x\u22122y \\leq 2x – 2y\u22642x\u22122<\/li>\n<\/ol>\n\n\n\n

    We are asked to determine which of the following ordered pairs satisfies both inequalities:<\/p>\n\n\n\n

      \n
    • (1,0)(1, 0)(1,0)<\/li>\n\n\n\n
    • (\u22121,1)(-1, 1)(\u22121,1)<\/li>\n\n\n\n
    • (2,2)(2, 2)(2,2)<\/li>\n<\/ul>\n\n\n\n

      Let\u2019s test each ordered pair one by one.<\/p>\n\n\n\n

      Test (1, 0):<\/h3>\n\n\n\n
        \n
      • For the first inequality, y>\u22123x+3y > -3x + 3y>\u22123x+3: 0>\u22123(1)+3\u21d20>\u22123+3\u21d20>0(False)0 > -3(1) + 3 \\quad \\Rightarrow \\quad 0 > -3 + 3 \\quad \\Rightarrow \\quad 0 > 0 \\quad (\\text{False})0>\u22123(1)+3\u21d20>\u22123+3\u21d20>0(False)<\/li>\n\n\n\n
      • For the second inequality, y\u22642x\u22122y \\leq 2x – 2y\u22642x\u22122: 0\u22642(1)\u22122\u21d20\u22642\u22122\u21d20\u22640(True)0 \\leq 2(1) – 2 \\quad \\Rightarrow \\quad 0 \\leq 2 – 2 \\quad \\Rightarrow \\quad 0 \\leq 0 \\quad (\\text{True})0\u22642(1)\u22122\u21d20\u22642\u22122\u21d20\u22640(True)<\/li>\n<\/ul>\n\n\n\n

        Since the first inequality is false, the pair (1,0)(1, 0)(1,0) does not satisfy both inequalities.<\/p>\n\n\n\n

        Test (-1, 1):<\/h3>\n\n\n\n
          \n
        • For the first inequality, y>\u22123x+3y > -3x + 3y>\u22123x+3: 1>\u22123(\u22121)+3\u21d21>3+3\u21d21>6(False)1 > -3(-1) + 3 \\quad \\Rightarrow \\quad 1 > 3 + 3 \\quad \\Rightarrow \\quad 1 > 6 \\quad (\\text{False})1>\u22123(\u22121)+3\u21d21>3+3\u21d21>6(False)<\/li>\n\n\n\n
        • For the second inequality, y\u22642x\u22122y \\leq 2x – 2y\u22642x\u22122: 1\u22642(\u22121)\u22122\u21d21\u2264\u22122\u22122\u21d21\u2264\u22124(False)1 \\leq 2(-1) – 2 \\quad \\Rightarrow \\quad 1 \\leq -2 – 2 \\quad \\Rightarrow \\quad 1 \\leq -4 \\quad (\\text{False})1\u22642(\u22121)\u22122\u21d21\u2264\u22122\u22122\u21d21\u2264\u22124(False)<\/li>\n<\/ul>\n\n\n\n

          Since both inequalities are false, the pair (\u22121,1)(-1, 1)(\u22121,1) does not satisfy both inequalities.<\/p>\n\n\n\n

          Test (2, 2):<\/h3>\n\n\n\n
            \n
          • For the first inequality, y>\u22123x+3y > -3x + 3y>\u22123x+3: 2>\u22123(2)+3\u21d22>\u22126+3\u21d22>\u22123(True)2 > -3(2) + 3 \\quad \\Rightarrow \\quad 2 > -6 + 3 \\quad \\Rightarrow \\quad 2 > -3 \\quad (\\text{True})2>\u22123(2)+3\u21d22>\u22126+3\u21d22>\u22123(True)<\/li>\n\n\n\n
          • For the second inequality, y\u22642x\u22122y \\leq 2x – 2y\u22642x\u22122: 2\u22642(2)\u22122\u21d22\u22644\u22122\u21d22\u22642(True)2 \\leq 2(2) – 2 \\quad \\Rightarrow \\quad 2 \\leq 4 – 2 \\quad \\Rightarrow \\quad 2 \\leq 2 \\quad (\\text{True})2\u22642(2)\u22122\u21d22\u22644\u22122\u21d22\u22642(True)<\/li>\n<\/ul>\n\n\n\n

            Since both inequalities are true, the pair (2,2)(2, 2)(2,2) satisfies both inequalities.<\/p>\n\n\n\n

            Conclusion:<\/h3>\n\n\n\n

            The correct ordered pair that satisfies both inequalities is (2,2)(2, 2)(2,2).<\/p>\n\n\n\n

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

            Which ordered pair makes both inequalities true? y > -3x + 3 y ? 2x – 2 (1,0) (-1,1) (2,2) The Correct Answer and Explanation is: We are given two inequalities: We are asked to determine which of the following ordered pairs satisfies both inequalities: Let\u2019s test each ordered pair one by one. Test (1, […]<\/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-265609","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265609","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=265609"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/265609\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=265609"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=265609"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=265609"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}