{"id":"cb_question_bank:76f2a39c-e009-44ff-8197-3b1aefe2fafb","source_id":"cb_question_bank","source_item_id":"76f2a39c-e009-44ff-8197-3b1aefe2fafb","external_id":"ab551853-877a-4560-a1dc-8c5843c3aa42","ibn":null,"question_id":"7dbd46d9","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of equations in two variables","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"8 x plus y equals negative 11 2 x squared equals y plus 341 The graphs of the equations in the given system of equations intersect at the point left parenthesis x comma y right parenthesis in the x y -plane. What is a possible value of x ?","stimulus":"","stimulus_html":null,"stem_html":"

\n\t\n\t\t\n\t\t\t8\n\t\t\tx\n\t\t\n\t\t+\n\t\ty\n\t\n\t=\n\t-11\n\n

\n

\n\t\n\t\t2\n\t\t\n\t\t\tx\n\t\t\t2\n\t\t\n\t\n\t=\n\t\n\t\ty\n\t\t+\n\t\t341\n\t\n\n

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The graphs of the equations in the given system of equations intersect at the point (x\n, y\n) in the \n\tx\n\ty\n\n-plane. What is a possible value of x\n?

","rationale_html":"

Choice A is correct. It's given that the graphs of the equations in the given system of equations intersect at the point x,y. Therefore, this intersection point is a solution to the given system. The solution can be found by isolating y\n in each equation. The given equation 8x+y=-11 can be rewritten to isolate y\n by subtracting \n\t8\n\tx\n\n from both sides of the equation, which gives y=-8x-11. The given equation 2x2=y+341 can be rewritten to isolate y\n by subtracting 341\n from both sides of the equation, which gives 2x2-341=y. With each equation solved for y\n, the value of y\n from one equation can be substituted into the other, which gives 2x2-341=-8x-11. Adding \n\t8\n\tx\n\n and 11\n to both sides of this equation results in 2x2+8x-330=0. Dividing both sides of this equation by 2\n results in x2+4x-165=0. This equation can be rewritten by factoring the left-hand side, which yields x+15x-11=0. By the zero-product property, if x+15x-11=0, then x+15=0, or x-11=0. It follows that x=-15, or x=11. Since only -15 is given as a choice, a possible value of x\n is -15. 

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Choice B is incorrect and may result from conceptual or calculation errors.

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Choice C is incorrect and may result from conceptual or calculation errors.

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Choice D is incorrect and may result from conceptual or calculation errors.

","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.824000+00:00","source_updated_at":"2023-08-02T20:25:59.824000+00:00","options":[{"label":"A","content_html":"

-15\n

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

-11\n

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

2\n

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

8\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}}