{"id":"cb_question_bank:fef99200-de97-49cb-8878-76bce36182d9","source_id":"cb_question_bank","source_item_id":"fef99200-de97-49cb-8878-76bce36182d9","external_id":null,"ibn":"10589-DC","question_id":"948087f2","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following ordered pairs ( x , y ) satisfies the system of inequalities above?","stimulus":"y is less than or equal to, 3 x plus 1 x minus y is greater than 1","stimulus_html":"<div class=\"stimulus_reference \">\n\t<table class=\"table_Borderless\"><tbody><tr><td class=\"tcp-2344cffe-5914-443c-959a-e13d8ae615b4\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c058e23dd1539446d15034ca2c359bf3cee0dabecb7513d686f3edf13c86c8e0\" alt=\"y is less than or equal to, 3 x plus 1\"></span></td>\n\t\t\t</tr><tr><td class=\"para_right tcp-504e9a8b-1d7f-4583-810f-d5248c190855\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ad7ed7c655edf525708d79c4cd732da47fb7f9123760ac0381d1ace3cf3b3baf\" alt=\"x minus y is greater than 1\"></span></td>\n\t\t\t</tr></tbody></table></div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following ordered pairs&nbsp;(<span class=\"italic\">x</span>, <span class=\"italic\">y</span>) satisfies the system of inequalities above?</p>\n","rationale_html":"<p>Choice D is correct. Any point (<span class=\"italic\">x</span>, <span class=\"italic\">y</span>) that is a solution to the given system of inequalities must satisfy both inequalities in the system. The second inequality in the system can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/22a93bc10013ef3c03aae9a4459f553cca72a0fc5fee6337472d0d6b9a322893\" alt=\"x is greater than, y plus 1\"></span>. Of the given answer choices, only choice D satisfies this inequality, because inequality <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/45a78bdd829e45f56a905fac147b286d879fb3641f8f1dd38929b646da924726\" alt=\"2 is greater than, negative 1 plus 1\"></span> is a true statement. The point <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5484feaff349a3121b4ea7ed30cc302306743d82d03a84e6a922631f62398fd2\" alt=\"with coordinates 2 comma negative 1\"></span> also satisfies the first inequality.</p><p>Alternate approach: Substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5484feaff349a3121b4ea7ed30cc302306743d82d03a84e6a922631f62398fd2\" alt=\"the ordered pair 2 comma negative 1\"></span> into the first inequality gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/082bcfcf489429754b7468db2188b197d4dc81693f2c4daf3d78222ff0e8649c\" alt=\"negative 1 is less than or equal to, 3 times 2, plus 1\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0be1280bb1e24616d37cc0722708136a4fbd4542b38726ee9032f7f5653a0b6a\" alt=\"negative 1 is less than or equal to 7\"></span>, which is a true statement. Substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5484feaff349a3121b4ea7ed30cc302306743d82d03a84e6a922631f62398fd2\" alt=\"the ordered pair 2 comma negative 1\"></span> into the second inequality gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bd0e9200684ef904bcca8662437883aa8f1feb2fa96821c2bed2269b8414ac57\" alt=\"2 minus negative 1, is greater than 1\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/28894eb6e5a9a9398be16023f86618e24857bf475b10461d2f4c5bcd08d25fa6\" alt=\"3 is greater than 1\"></span>, which is a true statement. Therefore, since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5484feaff349a3121b4ea7ed30cc302306743d82d03a84e6a922631f62398fd2\" alt=\"the ordered pair 2 comma negative 1\"></span> satisfies both inequalities, it is a solution to the system.</p><p>Choice A is incorrect because substituting −2 for <span class=\"italic\">x</span> and −1 for <span class=\"italic\">y</span> in the first inequality gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4012244284969021a4e664e2dc227c0e99703eb256fd949c3913a612fcc59c49\" alt=\"negative 1 is less than or equal to, 3 times negative 2, plus 1\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/aa6525506351dd93e5efa2e49017ed58b446f38c4c6983fac5c940f07e7f62c0\" alt=\"negative 1 is less than or equal to negative 5\"></span>, which is false. Choice B is incorrect because substituting −1 for <span class=\"italic\">x</span> and 3 for <span class=\"italic\">y</span> in the first inequality gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5307547a8db8dae49537f4d6e887ba1aab66ba7a3b4bc816b8f9928709566f7b\" alt=\"3 is less than or equal to, 3 times negative 1, plus 1\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/21760a38ec84e7bbce00c05e5f7fcfd86e4f785537d634e637c6a940e7041428\" alt=\"3 is less than or equal to negative 2\"></span>, which is false. Choice C is incorrect because substituting 1 for <span class=\"italic\">x</span> and 5 for <span class=\"italic\">y</span> in the first inequality gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/abe3d6776307f34cb1cbe343e86fa88c0734fe73a34bdd20919eea9b8fa695aa\" alt=\"5 is less than or equal to, 3 times 1, plus 1\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fb9184c2910da5791bf4922042f7be0384d6334b8bc2a8986147652dd84cc530\" alt=\"5 is less than or equal to 4\"></span>, which is false.</p><p>&nbsp;</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":true,"source_created_at":"2023-08-02T20:25:59.638000+00:00","source_updated_at":"2023-08-02T20:25:59.638000+00:00","options":[{"label":"A","content_html":"<p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1f22194e7fdea935d20f2d4e9119949714459df59b4b8f5eed5921da8e18b254\" alt=\"negative 2 comma negative 1\"></span></p><p>&nbsp;</p><p></p>\n","ord":0},{"label":"B","content_html":"<p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/30f9267ad013a559b3a79cac94423da094741be6ef0d165f4c297d0c4dab399d\" alt=\"negative 1 comma 3\"></span></p><p>&nbsp;</p><p></p>\n","ord":1},{"label":"C","content_html":"<p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/401013dcc8a9963a15648d9e44fc062687dcaec6e45345b4d5e765e2a239cb9a\" alt=\"1 comma 5\"></span></p><p>&nbsp;</p><p></p>\n","ord":2},{"label":"D","content_html":"<p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5484feaff349a3121b4ea7ed30cc302306743d82d03a84e6a922631f62398fd2\" alt=\"2 comma negative 1\"></span></p><p>&nbsp;</p><p></p>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}