{"id":"cb_question_bank:473ba0ae-2e27-4eb0-83ed-ba1a8f79edfc","source_id":"cb_question_bank","source_item_id":"473ba0ae-2e27-4eb0-83ed-ba1a8f79edfc","external_id":"0fe484a0-8389-4fe5-93dd-5d56c07a7c9c","ibn":null,"question_id":"aff28230","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"E","score_band":1,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"x equals 10 y equals x plus 21 The solution to the given system of equations is left parenthesis x comma y right parenthesis . What is the value of y ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"x equals 10\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>10</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: center;\"><math alttext=\"y equals x plus 21\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mi>x</mi>\n\t\t<mo>+</mo>\n\t\t<mn>21</mn>\n\t</mrow>\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=\"y\"><mi>y</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. It's given by the first equation in the given system of equations that <math alttext=\"x equals 10\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>10</mn>\n</mrow>\n</math>. Substituting <math alttext=\"10\"><mn>10</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the second equation in the given system yields <math alttext=\"y equals 10 plus 21\"><mi>y</mi><mo>=</mo><mn>10</mn><mo>+</mo><mn>21</mn></math>, or <math alttext=\"y equals 31\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mn>31</mn>\n</mrow>\n</math>. Therefore, the value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"31\"><mn>31</mn>\n</math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This is the value of <math alttext=\"x\"><mi>x</mi>\n</math>, not the value of <math alttext=\"y\"><mi>y</mi>\n</math>.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["D"],"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=\"2.1\"><mn>2.1</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"10\"><mn>10</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"21\"><mn>21</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"31\"><mn>31</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}}