{"id":"cb_question_bank:a065a22a-bed3-4ccf-8969-ba6f5f4ff771","source_id":"cb_question_bank","source_item_id":"a065a22a-bed3-4ccf-8969-ba6f5f4ff771","external_id":"425d30d9-246b-4058-b45c-2e4168f92a0f","ibn":null,"question_id":"f718c9cf","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"H","score_band":6,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"5 x plus 14 y equals 45 10 x plus 7 y equals 27 The solution to the given system of equations is left parenthesis x comma y right parenthesis . What is the value of x y ?","stimulus":"","stimulus_html":null,"stem_html":"

\n\t\n\t\t\n\t\t\t5\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t14\n\t\t\ty\n\t\t\n\t\n\t=\n\t45\n\n

\n

\n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t27\n\n

\n

The solution to the given system of equations is x,y. What is the value of \n\tx\n\ty\n\n?

","rationale_html":"

The correct answer is \n\t9\n\t5\n\n. Multiplying the first equation in the given system by 2\n yields \n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t28\n\t\t\ty\n\t\t\n\t\n\t=\n\t90\n\n. Subtracting the second equation in the given system, \n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t27\n\n, from \n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t28\n\t\t\ty\n\t\t\n\t\n\t=\n\t90\n\n yields 10x+28y-10x+7y=90-27, which is equivalent to 10x+28y-10x-7y=63, or \n\t\n\t\t21\n\t\ty\n\t\n\t=\n\t63\n\n. Dividing both sides of this equation by 21\n yields \n\ty\n\t=\n\t3\n\n. The value of x\n can be found by substituting 3\n for y\n in either of the two given equations. Substituting 3\n for y\n in the equation \n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t\n\t\t\t7\n\t\t\ty\n\t\t\n\t\n\t=\n\t27\n\n yields 10x+73=27, or \n\t\n\t\t\n\t\t\t10\n\t\t\tx\n\t\t\n\t\t+\n\t\t21\n\t\n\t=\n\t27\n\n. Subtracting 21\n from both sides of this equation yields \n\t\n\t\t10\n\t\tx\n\t\n\t=\n\t6\n\n. Dividing both sides of this equation by 10\n yields x=610, or \n\tx\n\t=\n\t\n\t\t3\n\t\t5\n\t\n\n. Therefore, the value of \n\tx\n\ty\n\n is 353, or 95. Note that 9/5 and 1.8 are examples of ways to enter a correct answer.

","correct_answer":["1.8","9/5"],"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":[],"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}}