{"id":246052,"date":"2025-07-06T17:54:12","date_gmt":"2025-07-06T17:54:12","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=246052"},"modified":"2025-07-06T17:54:15","modified_gmt":"2025-07-06T17:54:15","slug":"the-graph-shows-a-system-of-inequalities","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/06\/the-graph-shows-a-system-of-inequalities\/","title":{"rendered":"The graph shows a system of inequalities."},"content":{"rendered":"\n
The graph shows a system of inequalities. Which system is represented in the graph? Oy > x\u00b2-2x-3 y > x + 3 Oy < x\u00b2-2x-3 y < x + 3 Oy ? x\u00b2-2x-3 y ? x + 3 Oy > x\u00b2-2x-3 y<x+3<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
From your description, it sounds like you’re trying to identify a system of inequalities based on a graph. Let’s break down the possible options and the reasoning behind each one.<\/p>\n\n\n\n
Understanding the inequalities:<\/h3>\n\n\n\n\n
Oy > x\u00b2 – 2x – 3<\/strong>: This inequality represents a region above<\/strong> the parabola given by y=x2\u22122x\u22123y = x^2 – 2x – 3y=x2\u22122x\u22123. This is a parabola that opens upwards<\/strong>, and the inequality indicates that the solution lies above<\/strong> the curve.<\/li>\n\n\n\n
y > x + 3<\/strong>: This is a straight line with slope 1 and a y-intercept of 3. The inequality represents the region above<\/strong> this line.<\/li>\n\n\n\n
Oy < x\u00b2 – 2x – 3<\/strong>: This inequality represents the region below<\/strong> the parabola y=x2\u22122x\u22123y = x^2 – 2x – 3y=x2\u22122x\u22123, which is a parabola that opens upwards.<\/li>\n\n\n\n
y < x + 3<\/strong>: This inequality represents the region below<\/strong> the line y=x+3y = x + 3y=x+3.<\/li>\n<\/ol>\n\n\n\n
Interpreting the graph:<\/h3>\n\n\n\n
\n
If the graph shows a region above<\/strong> the parabola y=x2\u22122x\u22123y = x^2 – 2x – 3y=x2\u22122x\u22123 and below<\/strong> the line y=x+3y = x + 3y=x+3, the correct system of inequalities would be:\n
\n
Oy > x\u00b2 – 2x – 3<\/strong> (Region above the parabola)<\/li>\n\n\n\n
y < x + 3<\/strong> (Region below the line)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
Explanation:<\/h3>\n\n\n\n
\n
The graph’s shading indicates which side of the curve or line is included in the solution.<\/li>\n\n\n\n
If the shaded region is above<\/strong> the parabola y=x2\u22122x\u22123y = x^2 – 2x – 3y=x2\u22122x\u22123, the inequality for the parabola will be y>x2\u22122x\u22123y > x^2 – 2x – 3y>x2\u22122x\u22123, since the solution is above the curve.<\/li>\n\n\n\n
If the shaded region is below<\/strong> the line y=x+3y = x + 3y=x+3, then the inequality for the line will be y<x+3y < x + 3y<x+3, since the solution is below the line.<\/li>\n<\/ul>\n\n\n\n
Thus, the system represented by the graph is:<\/p>\n\n\n\n
\n
Oy > x\u00b2 – 2x – 3<\/strong><\/li>\n\n\n\n
y < x + 3<\/strong><\/li>\n<\/ul>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
The graph shows a system of inequalities. Which system is represented in the graph? Oy > x\u00b2-2x-3 y > x + 3 Oy < x\u00b2-2x-3 y < x + 3 Oy ? x\u00b2-2x-3 y ? x + 3 Oy > x\u00b2-2x-3 y<x+3 The Correct Answer and Explanation is: From your description, it sounds like you’re […]<\/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-246052","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246052","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=246052"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/246052\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=246052"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=246052"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=246052"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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