{"id":"cb_question_bank:284408e1-c764-4300-823f-196992b5b7be","source_id":"cb_question_bank","source_item_id":"284408e1-c764-4300-823f-196992b5b7be","external_id":"dce39b31-9110-4b75-93ff-5d7da57a6adc","ibn":null,"question_id":"7efe5495","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":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"y equals 3 x 2 x plus y equals 12 The solution to the given system of equations is left parenthesis x comma y right parenthesis . What is the value of 5 x ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"y equals 3 x\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>3</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n</mrow>\n</math></p>\n<p style=\"text-align: center;\"><math alttext=\"2 x plus y equals 12\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>2</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mi>y</mi>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>12</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: left;\">The solution to the given system of equations is <math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math>. What is the value of <math alttext=\"5 x\"><mrow>\n\t<mn>5</mn>\n\t<mi>x</mi>\n</mrow>\n</math>?</p>","rationale_html":"<p>Choice C is correct. It's given by the first equation in the system that <math alttext=\"y equals 3 x\"><mi>y</mi><mo>=</mo><mn>3</mn><mi>x</mi></math>. Substituting <math alttext=\"3 x\"><mrow>\n\t<mn>3</mn>\n\t<mi>x</mi>\n</mrow>\n</math> for <math alttext=\"y\"><mi>y</mi>\n</math> in the equation <math alttext=\"2 x plus y equals 12\"><mn>2</mn><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>12</mn></math> yields <math alttext=\"2 x plus 3 x equals 12\"><mn>2</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>x</mi><mo>=</mo><mn>12</mn></math>, or&nbsp;<math alttext=\"5 x equals 12\"><mn>5</mn><mi>x</mi><mo>=</mo><mn>12</mn></math>.&nbsp;</p>\n<p>Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.817000+00:00","source_updated_at":"2023-08-02T20:25:59.817000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"24\"><mn>24</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"15\"><mn>15</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"12\"><mn>12</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"5\"><mn>5</mn>\n</math></p>","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}}