{"id":"cb_question_bank:6960b5d1-b11e-4976-b62b-28dc3fe3e76c","source_id":"cb_question_bank","source_item_id":"6960b5d1-b11e-4976-b62b-28dc3fe3e76c","external_id":null,"ibn":"029346-DC","question_id":"52cb8ea4","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If the ordered pair x comma y is the solution to the system of equations above, what is the value of 3 x plus 3 y ?","stimulus":"Equation 1: 7 x minus 5 y, equals 4. Equation 2: 4 x minus 8 y, equals 9.","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/e7ba3908ed81691ec34563accb4627f4b6c780d125131ae4b689e6896332a725\" alt=\"Equation 1: 7 x minus 5 y, equals 4. Equation 2: 4 x minus 8 y, equals 9.\"></span></span></p>\n</div>\n","stem_html":"<p class=\"stem_paragraph \">If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/338db7e3a31d3afebe84d6ca556e60cbe33b3baf49002acc912917c4ff25d31e\" alt=\"the ordered pair x comma y \"></span></span> is the solution to the system of equations above, what is the value of&nbsp;<span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cbae6c5db20126f0c8874e324aed0223e15db040c8f3eb0d058e26369fd3159d\" alt=\"3 x plus 3 y\"></span>&nbsp;</span>?</p>\n","rationale_html":"<p>Choice B is correct. Subtracting the second equation, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8355537a9c4613586326ed97ed3e4d7692cdd6492c6b07a40ed2fa869a24fd9c\" alt=\"4 x minus 8 y, equals 9\"></span>, from the first equation, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/02479ec92290a75a1421e1510f8257dc86db8074e35d793ecd7b9ba1503274bc\" alt=\"7 x minus 5 y, equals 4\"></span>, results in <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c87c8a4e92c90e4f6765977adba74b10db41543a40f0ad76bd346885579bb9a0\" alt=\"open parenthesis, 7 x minus 5 y, close parenthesis, minus, open parenthesis, 4 x minus 8 y, close parenthesis, equals, 4 minus 9\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5c1f577353669e3cb36a86d7b9e16b972873d633275d9701899c2198262a2351\" alt=\"7 x minus 5 y, minus 4 x, plus 8 y, equals 5\"></span>. Combining like terms on the left-hand side of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a57f97b055ea573db5cd4917ad6cd7c1c570ec8826664d6bf24d65f19f4c4fa6\" alt=\"3 x plus 3 y, equals negative 5\"></span>.</p><p>Choice A is incorrect and may result from miscalculating <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cfca65a62acea3390490ea6ee2ddaf2095779b6fff80261b2c4a8426bb876f63\" alt=\"4 minus 9 \"></span> as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7b91f231e344281646dd4b239f6905feb88d2bc746ff8d42a2fdb8dda223630c\" alt=\"negative 13\"></span>. Choice C is incorrect and may result from miscalculating <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cfca65a62acea3390490ea6ee2ddaf2095779b6fff80261b2c4a8426bb876f63\" alt=\"4 minus 9 \"></span> as 5. Choice D is incorrect and may result from adding 9 to 4 instead of subtracting 9 from 4.</p><p>&nbsp;</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.624000+00:00","source_updated_at":"2023-08-02T20:25:59.624000+00:00","options":[{"label":"A","content_html":"<p><span class=\"choice_cell align:right \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7b91f231e344281646dd4b239f6905feb88d2bc746ff8d42a2fdb8dda223630c\" alt=\"negative 13\"></span></span> </span></p>\n","ord":0},{"label":"B","content_html":"<p><span class=\"choice_cell align:right \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/143ecd6752fff253d223e7404295e24d105d344680b21ec83f900c5115d98d48\" alt=\"negative 5\"></span></span> </span></p>\n","ord":1},{"label":"C","content_html":"<p><span class=\"choice_cell align:right \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/da81f995fde566bcfccbb13c76f46067fe002f64e918e950c3158cbc4c5a0da9\" alt=\"5\"></span></span> </span></p>\n","ord":2},{"label":"D","content_html":"<p><span class=\"choice_cell align:right \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a017ed9a1a9530f0ea8cbd3ac63d72fb98d374b9ca259a9de917ba7cb4c6e8af\" alt=\"13\"></span></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}}