{"id":"cb_question_bank:c32ce35c-b001-4aad-8fb4-1dc7076f6bcc","source_id":"cb_question_bank","source_item_id":"c32ce35c-b001-4aad-8fb4-1dc7076f6bcc","external_id":null,"ibn":"08687-DC","question_id":"5e422ff9","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the solution to the system of equations above, what is the value of y ?","stimulus":"y equals, 2 x minus 3, and, 3 y equals 5 x","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6265f03abd8d7f75860fb4744fca35de782bfa07768abaed9f36b5dcde3a6011\" alt=\"y equals, 2 x minus 3, and, 3 y equals 5 x\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">In the solution to the system of equations above, what is the value of <span class=\"italic\">y</span> ?</p>\n","rationale_html":"<p>Choice D is correct. Multiplying both sides of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/07b5d2b00b4e5045e8a1323d829a593ef8ae8a8c1148882174c56cdae2c2f285\" alt=\"y equals 2 x minus 3\"></span> by 5 results in <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e07bb48d1a8076b99493af2c417f67b9eb1bf7851a9764d665408edc05b2da3b\" alt=\"5 y, equals 10 x minus 15\"></span>. Multiplying both sides of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3773e3cd088c73f4b30d626563288e53749d97f7dd1a9e0fed6d90ec7120790d\" alt=\"3 y, equals 5 x\"></span><span class=\"italic\"></span> by 2 results in <span class=\"italic\"></span><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/457a2a3c5af64c49309cdd54b423088a0e985f1679566f54b615089e7be4b479\" alt=\"6 y, equals 10 x\"></span>. Subtracting the resulting equations yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3fef1c01267c58884c93a85212b61a9e04860847c0357b26e5033a714c7f5c40\" alt=\"5 y minus 6 y, equals, open parenthesis, 10 x minus 15, close parenthesis, minus, 10 x\"></span>, which simplifies to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/000c2d97fd3911160412fd07daef2758a4c15d74165944d089754883f8b5a529\" alt=\"negative y equals negative 15\"></span>. Dividing both sides of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/000c2d97fd3911160412fd07daef2758a4c15d74165944d089754883f8b5a529\" alt=\"negative y equals negative 15\"></span> by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1e573ec087416273e06563cee97890abeeed317436562b06a92c8920d4c759d\" alt=\"negative 1\"></span> results in <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f52c8aa3e5f94ebd1d3f02fb933205f46b8fd0a11c0584851cc5fab3b205ecf3\" alt=\"y equals 15\"></span>.</p><p>Choices A and B are incorrect and may result from incorrectly subtracting the transformed equation. Choice C is incorrect and may result from finding the value of <span class=\"italic\">x</span> instead of the value of <span class=\"italic\">y</span>.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.636000+00:00","source_updated_at":"2023-08-02T20:25:59.636000+00:00","options":[{"label":"A","content_html":"<span class=\"choice_cell align:right \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dc64c40ddba51ce61b96471847a6e4bebd3dd9399827ec9626b64d71319edea9\" alt=\"negative 15\"></span></span>\n          </span>\n","ord":0},{"label":"B","content_html":"<span class=\"choice_cell align:right \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/85427db1337a88f32c150849afd30d75356f31a9f7c40b1e77f5872ce3416796\" alt=\"negative 9\"></span></span>\n          </span>\n","ord":1},{"label":"C","content_html":"<span class=\"choice_cell align:right \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6ef2dfc2e9800c5db0bef6e583328fff9c74c529012681f4f6096056e97f3751\" alt=\"9\"></span></span>\n          </span>\n","ord":2},{"label":"D","content_html":"<span class=\"choice_cell align:right \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a94338896b7f7978fafc9ea30f0accb9ad88788989f24306e84c00eb9454975f\" alt=\"15\"></span></span>\n          </span>\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}}