{"id":"cb_question_bank:92f1eea8-c905-4a15-954e-286f2fb34a49","source_id":"cb_question_bank","source_item_id":"92f1eea8-c905-4a15-954e-286f2fb34a49","external_id":"87828f3a-da5a-4eeb-9cec-04f0ff9e1f97","ibn":null,"question_id":"d909cd31","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":"minus 15 x plus 25 y equals 65 One of the two equations in a system of linear equations is given. The system has infinitely many solutions. Which of the following could be the second equation in the system?","stimulus":"","stimulus_html":null,"stem_html":"

\n\t\n\t\t\n\t\t\t-\n\t\t\t15\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t25\n\t\t\ty\n\t\t\n\t\n\t=\n\t65\n\n

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One of the two equations in a system of linear equations is given. The system has infinitely many solutions. Which of the following could be the second equation in the system?

","rationale_html":"

Choice C is correct. It's given that the system has infinitely many solutions. A system of two linear equations has infinitely many solutions when the two linear equations are equivalent. Dividing both sides of the given equation by 5\n yields \n\t\n\t\t\n\t\t\t-\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t5\n\t\t\ty\n\t\t\n\t\n\t=\n\t13\n\n. Dividing both sides of choice C by 4\n also yields \n\t\n\t\t\n\t\t\t-\n\t\t\t3\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t5\n\t\t\ty\n\t\t\n\t\n\t=\n\t13\n\n, so choice C is equivalent to the given equation. Thus, choice C could be the second equation in the system.

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Choice A is incorrect. The system consisting of this equation and the given equation has one solution, not infinitely many solutions.

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Choice B is incorrect. The system consisting of this equation and the given equation has one solution, not infinitely many solutions.

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Choice D is incorrect. The system consisting of this equation and the given equation has no solution, not infinitely many solutions.

","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.818000+00:00","source_updated_at":"2023-08-02T20:25:59.818000+00:00","options":[{"label":"A","content_html":"

\n\t\n\t\t\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t20\n\t\t\ty\n\t\t\n\t\n\t=\n\t52\n\n

","ord":0},{"label":"B","content_html":"

\n\t\n\t\t\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t20\n\t\t\ty\n\t\t\n\t\n\t=\n\t-52\n\n

","ord":1},{"label":"C","content_html":"

\n\t\n\t\t\n\t\t\t-\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t20\n\t\t\ty\n\t\t\n\t\n\t=\n\t52\n\n

","ord":2},{"label":"D","content_html":"

\n\t\n\t\t\n\t\t\t-\n\t\t\t12\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t20\n\t\t\ty\n\t\t\n\t\n\t=\n\t-52\n\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}}