{"id":"cb_question_bank:3c99ae45-761f-4502-8b01-a175f4094aea","source_id":"cb_question_bank","source_item_id":"3c99ae45-761f-4502-8b01-a175f4094aea","external_id":"f0975e35-afbb-4d74-9091-7a06a2bf4d03","ibn":null,"question_id":"317e80f9","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":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"x plus y equals 18 5 y equals x What is the solution left parenthesis x comma y right parenthesis to the given system of equations?","stimulus":"","stimulus_html":null,"stem_html":"

\n\t\n\t\tx\n\t\t+\n\t\ty\n\t\n\t=\n\t18\n\n

\n

\n\t\n\t\t5\n\t\ty\n\t\n\t=\n\tx\n\n

\n

What is the solution x,y to the given system of equations?

","rationale_html":"

Choice A is correct. The second equation in the given system defines the value of x\n as \n\t5\n\ty\n\n. Substituting \n\t5\n\ty\n\n for x\n into the first equation yields 5y+y=18 or 6y=18. Dividing each side of this equation by 6\n yields \n\ty\n\t=\n\t3\n\n. Substituting 3\n for y\n in the second equation yields 53=x or x=15. Therefore, the solution x,y to the given system of equations is 15,3. 

\n

Choice B is incorrect. Substituting 16\n for x\n and 2\n for y\n in the second equation yields 52=16, which is not true. Therefore, 16,2 is not a solution to the given system of equations.

\n

Choice C is incorrect. Substituting 17\n for x\n and 1\n for y\n in the second equation yields 51=17, which is not true. Therefore, 17,1 is not a solution to the given system of equations.

\n

Choice D is incorrect. Substituting 18\n for x\n and 0\n for y\n in the second equation yields 50=18, which is not true. Therefore, 18,0 is not a solution to the given system of equations.

","correct_answer":["A"],"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":"

15,3

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

16,2

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

17,1

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

18,0

","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}}