{"id":"cb_question_bank:351701f2-411f-43ef-8680-fba54dbbe043","source_id":"cb_question_bank","source_item_id":"351701f2-411f-43ef-8680-fba54dbbe043","external_id":null,"ibn":"032729-DC","question_id":"968e9e51","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 comma y is a solution to the system of inequalities above?","stimulus":"Inequality 1: y is less than or equal to x. Inequality 2: y is less than or equal to negative x.","stimulus_html":"<div class=\"stimulus_reference \">\n\t<p class=\"standalone_statement style:1 \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cdfd683a14e9cce86c0d96a1e458a4dbdadbdf00c2c511ae0a8c0ad459b0f100\" alt=\"Inequality 1: y is less than or equal to x.\"></span></span></p>\n\n\t<p class=\"standalone_statement style:1 \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b51559dbff99033d48a360e36ba50731aedea0a009771a57ec258545f000dd81\" alt=\"Inequality 2: y is less than or equal to negative x.\"></span></span></p>\n</div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following ordered pairs <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/338db7e3a31d3afebe84d6ca556e60cbe33b3baf49002acc912917c4ff25d31e\" alt=\"x comma y \"></span></span> is a solution to the system of inequalities above?</p>\n","rationale_html":"<p>Choice D is correct. The solutions to the given system of inequalities is the set of all ordered pairs <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/29eda5c740cd27d857d88b32b6e6a8a1d263911ac678e319dd0387efa41b0e58\" alt=\"x comma y \"></span> that satisfy both inequalities in the system. For an ordered pair to satisfy the inequality <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cdfd683a14e9cce86c0d96a1e458a4dbdadbdf00c2c511ae0a8c0ad459b0f100\" alt=\"y is less than or equal to x\"></span>, the value of the ordered pair’s <span class=\"italic\">y</span>-coordinate must be less than or equal to the value of the ordered pair’s <span class=\"italic\">x</span>-coordinate. This is true of the ordered pair <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f3a617dc5174862cc5fa8e2981f8d8f3be75ed78138f62001f8a3305f04ce284\" alt=\"0 comma negative 1\"></span>, because <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/62cffd73f0ab846b1e85eb9967306525eb108249c1c30730738d982fffcfa8ee\" alt=\"negative 1 is less than or equal to 0\"></span>. To satisfy the inequality <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b51559dbff99033d48a360e36ba50731aedea0a009771a57ec258545f000dd81\" alt=\"y is less than or equal to negative x\"></span>, the value of the ordered pair’s <span class=\"italic\">y</span>-coordinate must be less than or equal to the value of the additive inverse of the ordered pair’s <span class=\"italic\">x</span>-coordinate. This is also true of the ordered pair <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f3a617dc5174862cc5fa8e2981f8d8f3be75ed78138f62001f8a3305f04ce284\" alt=\"0 comma negative 1\"></span>. Because 0 is its own additive inverse, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/070d4820dc9c57cb1d9833edda5827dd3a298e548d055e0880067181a8fd7964\" alt=\"negative 1 is less than or equal to the negative of 0\"></span>&nbsp;is the same as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/62cffd73f0ab846b1e85eb9967306525eb108249c1c30730738d982fffcfa8ee\" alt=\"negative 1 is less than or equal to 0\"></span>. Therefore, the ordered pair <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f3a617dc5174862cc5fa8e2981f8d8f3be75ed78138f62001f8a3305f04ce284\" alt=\"0 comma negative 1\"></span> is a solution to the given system of inequalities.</p><p>Choice A is incorrect. This ordered pair satisfies only the inequality <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cdfd683a14e9cce86c0d96a1e458a4dbdadbdf00c2c511ae0a8c0ad459b0f100\" alt=\"y is less than or equal to x\"></span> in the given system, not both inequalities. Choice B incorrect. This ordered pair satisfies only the inequality <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b51559dbff99033d48a360e36ba50731aedea0a009771a57ec258545f000dd81\" alt=\"y is less than or equal to negative x\"></span> in the system, but not both inequalities. Choice C is incorrect. This ordered pair satisfies neither inequality.</p><p>&nbsp;</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.627000+00:00","source_updated_at":"2023-08-02T20:25:59.627000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dd517ff65ad53662b01847047d12b83dfb628a81d6983d27b71cf476b5e02ccf\" alt=\"1 comma 0\"></span></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f26815be355fc45d23ae5e83cd8f1f22ffb633986a89066e50cdfd4d33952873\" alt=\"negative 1 comma 0\"></span></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6f3a9226f302010cb970c4c9a7ec50c741c7d5a2c55111fb791bcf92be5e5159\" alt=\"0 comma 1\"></span></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f3a617dc5174862cc5fa8e2981f8d8f3be75ed78138f62001f8a3305f04ce284\" alt=\"0 comma negative 1\"></span></span></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}}