{"id":"cb_practice_pdf:t8-math-m1-q22","source_id":"cb_practice_pdf","source_item_id":"t8-math-m1-q22","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-8","module_number":1,"position":22,"stem":"- - - -_≤_x+7 - - ~ y y ≥ −2x−1 (x,y) Which point is a solution to the given system of inequalities in the xy-plane? (−14,0)","stimulus":"","stimulus_html":null,"stem_html":"<p>- - - -_≤_x+7 - - ~ y y ≥ −2x−1 (x,y) Which point is a solution to the given system of inequalities in the xy-plane? (−14,0)</p>","rationale_html":"<p>Choice D is correct. A point ^x,yh is a solution to a system of inequalities in the xy-plane if substituting the x-coordinate and the y-coordinate of the point for x and y, respectively, in each inequality makes both of the inequalities true. 14 Substituting the x-coordinate and the y-coordinate of choice D, and 0, for x # + and y, respectively, in the first inequality in the given system, y x 7, yields 0#14+7 0#21 14 , or , which is true. Substituting for x and 0 for y in the $-2 -1 0$-2 14 -1 second inequality in the given system, y x , yields ^ h , or 0$-29 14,0 , which is true. Therefore, the point ^ h is a solution to the given system of inequalities in the xy-plane. 37 SAT PRACTICE TEST #8 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 1 -14 Choice A is incorrect. Substituting for x and 0 for y in the inequality # + 0#-14+7 0#-7 y x 7 yields , or , which is not true. Choice B is incorrect. -14 $-2 -1 Substituting 0 for x and for y in the inequality y x yields -14$-2 0 -1 -14$-1 ^ h , or , which is not true. Choice C is incorrect. Substituting 14 # + 14#0+7 14#7 0 for x and for y in the inequality y x 7 yields , or , which is not true.</p>","correct_answer":["D"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>(0,−14)</p>","ord":0},{"label":"B","content_html":"<p>(0,14)</p>","ord":1},{"label":"C","content_html":"<p>(14,0)</p>","ord":2},{"label":"D","content_html":"","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}