{"id":"cb_question_bank:b3a9592e-cc4c-423c-a702-7f1ad0c4cd47","source_id":"cb_question_bank","source_item_id":"b3a9592e-cc4c-423c-a702-7f1ad0c4cd47","external_id":"7eab7aa7-dffb-49ed-89bb-e363db1aaad3","ibn":null,"question_id":"4ec95eab","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":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"y equals negative 3 x 4 x plus y equals 15 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=\"y equals negative 3 x\"><mi>y</mi><mo>=</mo><mrow><mo>-</mo><mn>3</mn></mrow><mi>x</mi></math></p>\n<p style=\"text-align: center;\"><math alttext=\"4 x plus y equals 15\"><mrow><mn>4</mn></mrow><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mrow><mn>15</mn></mrow></math></p>\n<p style=\"text-align: left;\">The solution to the given system of equations is&nbsp;<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>Choice C is correct. The given system of linear equations can be solved by the substitution method. Substituting <math alttext=\"minus 3 x\"><mo>-</mo><mn>3</mn><mi>x</mi></math>&nbsp;for <math alttext=\"y\"><mi>y</mi>\n</math> from the first equation in the given system into the second equation yields <math alttext=\"4 x plus left parenthesis minus 3 x right parenthesis equals 15\"><mn>4</mn><mi>x</mi><mo>+</mo><mfenced><mrow><mo>-</mo><mn>3</mn><mi>x</mi></mrow></mfenced><mo>=</mo><mn>15</mn></math>, or <math alttext=\"x equals 15\"><mi>x</mi><mo>=</mo><mn>15</mn></math>.</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. This is the absolute value of <math alttext=\"y\"><mi>y</mi>\n</math>, not the value of <math alttext=\"x\"><mi>x</mi>\n</math>.</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.819000+00:00","source_updated_at":"2023-08-02T20:25:59.819000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"1\"><mn>1</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"5\"><mn>5</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"15\"><mn>15</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"45\"><mn>45</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}}