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Students use the provided coordinate grids to graph boundary lines and shade the overlapping solution regions for the system, completing multiple numbered items on the 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of inequalities?",{"text":72,"@type":64},"Shade the region where the graphs of both inequalities overlap, since that intersection contains points that satisfy the entire system.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},522775,1791462986,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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solution to each system of inequalities.  \n1) y > 4x − 3 y ≥ −2x + 3  \n\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  | 5 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 4 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 3 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 2 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 1 |  |  |  |  |  |  |\n| − | 5 − | 4 | − | 3 | − | 2 | − | 1 0 |  | 1 | 2 | 3 | 4 5 |  |\n|  |  |  |  |  |  |  |  | −1 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −2 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −3 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −4 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | −5 |  |  |  |  |  |  |  |\n\n3) y \u003C 3  \ny ≤ − x + 1  \n\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  | 5 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 4 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 3 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 2 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 1 |  |  |  |  |  |  |\n| − | 5 − | 4 | − | 3 | − | 2 | − | 1 0 |  | 1 | 2 | 3 | 4 5 |  |\n|  |  |  |  |  |  |  |  | −1 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −2 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −3 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −4 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | −5 |  |  |  |  |  |  |  |\n\n2) y ≥ −5x + 3  \ny > −2  \n\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  | 5 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 4 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 3 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 2 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 1 |  |  |  |  |  |  |\n| − | 5 − | 4 | − | 3 | − | 2 | − | 1 0 |  | 1 | 2 | 3 | 4 5 |  |\n|  |  |  |  |  |  |  |  | −1 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −2 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −3 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −4 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | −5 |  |  |  |  |  |  |  |\n\n4) y ≥ x − 3 y ≥ − x − 1  \n\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  | 5 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 4 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 3 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 2 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 1 |  |  |  |  |  |  |\n| − | 5 − | 4 | − | 3 | − | 2 | − | 1 0 |  | 1 | 2 | 3 | 4 5 |  |\n|  |  |  |  |  |  |  |  | −1 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −2 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −3 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −4 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | −5 |  |  |  |  |  |  |  |\n\n5) x ≤ −3  \n5x + 3y ≥ −9  \n\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  | 5 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 4 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 3 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 2 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 1 |  |  |  |  |  |  |\n| − | 5 − | 4 | − | 3 | − | 2 | − | 1 0 |  | 1 | 2 | 3 | 4 5 |  |\n|  |  |  |  |  |  |  |  | −1 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −2 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −3 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | −4 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  | −5 |  |  |  |  |  |  |  |\n\n7) x + y > 2  \n2x − y > 1  \n\n|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  | 5 |  |  |  |  |  |  |\n|  |  |  |  |  |  |  |  | 4 |  |  |  |  |  |  |\n|  |  | ","cbCaijAHgthp0BBM","https://ap.wps.com/l/cbCaijAHgthp0BBM","pdf",156194,"English","# Sketching the solution to each system of inequalities\n## Problem 1: y > 4x - 3 and y ≥ -2x + 3\n## Problem 2: y ≥ -5x + 3 and y > -2\n## Problem 3: y \u003C 3 and y ≤ -x + 1\n## Problem 4: y ≥ x - 3 and y ≥ -x - 1\n## Problem 5: x ≤ -3 and 5x + 3y ≥ -9\n## Problem 6: 4x - 3y \u003C 9 and x + 3y > 6\n## Problem 7: x + y > 2 and 2x - y > 1\n## Problem 8: x + y ≥ 2 and 4x + y ≥ -1\n## Problem 9: 4x + 3y > -6 and x - 3y ≤ -9","[{\"question\":\"What does the worksheet ask students to do with each system of inequalities?\",\"answer\":\"Sketch the solution for each system by graphing the inequalities on the coordinate grid and identifying the overlap region that satisfies both.\"},{\"question\":\"How are strict and non-strict inequalities treated on the graph?\",\"answer\":\"Strict inequalities (\\u003e, \\u003c) use dashed boundary lines, while non-strict inequalities (≥, ≤) use solid boundary lines to show whether boundary points are included.\"},{\"question\":\"What should be shaded to represent the solution to a system of inequalities?\",\"answer\":\"Shade the region where the graphs of both inequalities overlap, since that intersection contains points that satisfy the entire system.\"}]","Kuta Software - Infinite Algebra 2 - Systems of Inequalities - Worksheet | PDF",1791426160,15]