{"id":"cb_question_bank:c671b60c-3257-424b-a40f-eea617e28e2a","source_id":"cb_question_bank","source_item_id":"c671b60c-3257-424b-a40f-eea617e28e2a","external_id":"e223b909-79a8-46de-a366-14993592a4c7","ibn":null,"question_id":"c8bf5313","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":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"x equals 8 y equals x squared plus 8 The graphs of the equations in the given system of equations intersect at the point left parenthesis x comma y right parenthesis in the xy -plane. What is the value of y ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"x equals 8\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>8</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: center;\"><math alttext=\"y equals x squared plus 8\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<msup>\n\t\t\t<mi>x</mi>\n\t\t\t<mn>2</mn>\n\t\t</msup>\n\t\t<mo>+</mo>\n\t\t<mn>8</mn>\n\t</mrow>\n</mrow>\n</math></p>\n<p style=\"text-align: left;\">The graphs of the equations in the given system of equations intersect at the point <math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math> in the <em>xy</em>-plane. What is the value of <math alttext=\"y\"><mi>y</mi>\n</math>?</p>","rationale_html":"<p>Choice D is correct. Since the graphs of the equations in the given system intersect at the point <math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math>, the point <math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math>&nbsp;represents a solution to the given system of equations. The first equation of the given system of equations states that <math alttext=\"x equals 8\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>8</mn>\n</mrow>\n</math>. Substituting <math alttext=\"8\"><mn>8</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the second equation of the given system of equations yields <math alttext=\"y equals 8 squared plus 8\"><mi>y</mi><mo>=</mo><msup><mn>8</mn><mn>2</mn></msup><mo>+</mo><mn>8</mn></math>, or <math alttext=\"y equals 72\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mn>72</mn>\n</mrow>\n</math>. Therefore, the value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"72\"><mn>72</mn>\n</math>.</p>\n<p>Choice A is incorrect. This is the value of <math alttext=\"x\"><mi>x</mi>\n</math>, not <math alttext=\"y\"><mi>y</mi>\n</math>.</p>\n<p>Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["D"],"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":"<p><math alttext=\"8\"><mn>8</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"24\"><mn>24</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"64\"><mn>64</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"72\"><mn>72</mn>\n</math></p>","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}}