{"id":"cb_question_bank:680e2c75-16e2-4d85-9a2b-e23243e72b39","source_id":"cb_question_bank","source_item_id":"680e2c75-16e2-4d85-9a2b-e23243e72b39","external_id":"96dd952c-8f39-4328-a087-4989624fb279","ibn":null,"question_id":"1362ccde","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":"y equals 4 x plus 1 4 y equals 15 x minus 8 The solution to the given system of equations is left parenthesis x comma y right parenthesis . What is the value of x minus y ?","stimulus":"","stimulus_html":null,"stem_html":"

\n\ty\n\t=\n\t\n\t\t\n\t\t\t4\n\t\t\tx\n\t\t\n\t\t+\n\t\t1\n\t\n\n
\n\t\n\t\t4\n\t\ty\n\t\n\t=\n\t\n\t\t\n\t\t\t15\n\t\t\tx\n\t\t\n\t\t-\n\t\t8\n\t\n\n

\n

The solution to the given system of equations is x,y. What is the value of x-y?

","rationale_html":"

The correct answer is 35\n. The first equation in the given system of equations defines y\n as 4x+1. Substituting 4x+1 for y\n in the second equation in the given system of equations yields 44x+1=15x-8. Applying the distributive property on the left-hand side of this equation yields 16x+4=15x-8. Subtracting \n\t15\n\tx\n\n from each side of this equation yields x+4=-8. Subtracting 4\n from each side of this equation yields x=-12. Substituting -12\n for x\n in the first equation of the given system of equations yields y=4-12+1, or y=-47. Substituting -12\n for x\n and -47\n for y\n into the expression x-y yields -12--47, or 35\n.

","correct_answer":["35"],"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":[],"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}}