{"id":"cb_question_bank:d47cb908-d2a6-4787-b161-6f8c7dc61a81","source_id":"cb_question_bank","source_item_id":"d47cb908-d2a6-4787-b161-6f8c7dc61a81","external_id":"a06c928d-bb2e-484a-9091-bfb1ee3246e4","ibn":null,"question_id":"e8779461","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":"M","score_band":4,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"y equals x squared plus 14 x plus 48 x plus 8 equals 11 The solution to the given system of equations is left parenthesis x comma y right parenthesis . What is the value of y ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"y equals x squared plus 14 x plus 48\"><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<mrow>\n\t\t\t<mn>14</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>48</mn>\n\t</mrow>\n</mrow>\n</math></p>\n<p style=\"text-align: center;\"><math alttext=\"x plus 8 equals 11\"><mrow>\n\t<mrow>\n\t\t<mi>x</mi>\n\t\t<mo>+</mo>\n\t\t<mn>8</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>11</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: left;\">The solution to the given system of equations is&nbsp;<math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math>. What is the value of <math alttext=\"y\"><mi>y</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"99\"><mn>99</mn>\n</math>. In the given system of equations, the second equation is <math alttext=\"x plus 8 equals 11\"><mi>x</mi><mo>+</mo><mn>8</mn><mo>=</mo><mn>11</mn></math>. Subtracting <math alttext=\"8\"><mn>8</mn>\n</math> from both sides of this equation yields <math alttext=\"x equals 3\"><mi>x</mi><mo>=</mo><mn>3</mn></math>. In the given system of equations, the first equation is <math alttext=\"y equals x squared plus 14 x plus 48\"><mi>y</mi><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>14</mn><mi>x</mi><mo>+</mo><mn>48</mn></math>. Substituting <math alttext=\"3\"><mn>3</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in this equation yields <math alttext=\"y equals left parenthesis 3 right parenthesis squared plus 14 left parenthesis 3 right parenthesis plus 48\"><mi>y</mi><mo>=</mo><msup><mfenced><mn>3</mn></mfenced><mn>2</mn></msup><mo>+</mo><mn>14</mn><mfenced><mn>3</mn></mfenced><mo>+</mo><mn>48</mn></math>, or&nbsp;<math alttext=\"y equals 99\"><mi>y</mi><mo>=</mo><mn>99</mn></math>. Therefore, the solution to the given system of equations is <math alttext=\"left parenthesis x comma y right parenthesis equals left parenthesis 3 comma 99 right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced><mo>=</mo><mfenced><mrow><mn>3</mn><mo>,</mo><mn>99</mn></mrow></mfenced></math>. Thus, the value of <math alttext=\"y\"><mi>y</mi>\n</math> is <math alttext=\"99\"><mn>99</mn>\n</math>.</p>","correct_answer":["99"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.823000+00:00","source_updated_at":"2023-08-02T20:25:59.823000+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}}