{"id":"cb_question_bank:f68f4bdd-f19a-44eb-8304-90f07cbf56ca","source_id":"cb_question_bank","source_item_id":"f68f4bdd-f19a-44eb-8304-90f07cbf56ca","external_id":"aa6865b9-fa65-43d3-bbf6-6e17250dc546","ibn":null,"question_id":"e53688cb","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":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"x plus 3 y equals 29 3 y equals 11 The solution to the given system of equations is left parenthesis x comma y right parenthesis . What is the value of x ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"x plus 3 y equals 29\"><mrow>\n\t<mrow>\n\t\t<mi>x</mi>\n\t\t<mo>+</mo>\n\t\t<mrow>\n\t\t\t<mn>3</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>29</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: center;\"><math alttext=\"3 y equals 11\"><mrow>\n\t<mrow>\n\t\t<mn>3</mn>\n\t\t<mi>y</mi>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>11</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=\"x\"><mi>x</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"18\"><mn>18</mn>\n</math>. It's given by the second equation in the system that <math alttext=\"3 y equals 11\"><mrow>\n\t<mrow>\n\t\t<mn>3</mn>\n\t\t<mi>y</mi>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>11</mn>\n</mrow>\n</math>. Substituting <math alttext=\"11\"><mn>11</mn>\n</math> for <math alttext=\"3 y\"><mrow>\n\t<mn>3</mn>\n\t<mi>y</mi>\n</mrow>\n</math> in the first equation in the system, <math alttext=\"x plus 3 y equals 29\"><mrow>\n\t<mrow>\n\t\t<mi>x</mi>\n\t\t<mo>+</mo>\n\t\t<mrow>\n\t\t\t<mn>3</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>29</mn>\n</mrow>\n</math>, yields <math alttext=\"x plus 11 equals 29\"><mrow>\n\t<mrow>\n\t\t<mi>x</mi>\n\t\t<mo>+</mo>\n\t\t<mn>11</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>29</mn>\n</mrow>\n</math>. Subtracting <math alttext=\"11\"><mn>11</mn>\n</math> from both sides of this equation yields <math alttext=\"x equals 18\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>18</mn>\n</mrow>\n</math>.</p>","correct_answer":["18"],"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":[],"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}}