{"id":"cb_question_bank:ffff47cc-dc03-44d8-aa01-94f588a44fdb","source_id":"cb_question_bank","source_item_id":"ffff47cc-dc03-44d8-aa01-94f588a44fdb","external_id":"7e4cd51c-5329-4e8b-83dd-1416f04a294f","ibn":null,"question_id":"58b109d4","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":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"x squared plus y plus 7 equals 7 20 x plus 100 minus y equals 0 The solution to the given system of equations is left parenthesis x comma y right parenthesis . What is the value of x ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"x squared plus y plus 7 equals 7\"><mrow>\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<mi>y</mi>\n\t\t<mo>+</mo>\n\t\t<mn>7</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>7</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: center;\"><math alttext=\"20 x plus 100 minus y equals 0\"><mrow><mn>20</mn></mrow><mi>x</mi><mo>+</mo><mrow><mn>100</mn></mrow><mo>-</mo><mi>y</mi><mo>=</mo><mn>0</mn></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=\"x\"><mi>x</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"negative 10\"><mo>-</mo><mn>10</mn>\n</math>. Adding <math alttext=\"y\"><mi>y</mi>\n</math> to both sides of the second equation in the given system yields <math alttext=\"20 x plus 100 equals y\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>20</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>100</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mi>y</mi>\n</mrow>\n</math>. Substituting <math alttext=\"20 x plus 100\"><mrow>\n\t<mrow>\n\t\t<mn>20</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>100</mn>\n</mrow>\n</math> for <math alttext=\"y\"><mi>y</mi>\n</math> in the first equation in the given system yields <math alttext=\"x squared plus 20 x plus 100 plus 7 equals 7\"><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>20</mn><mi>x</mi><mo>+</mo><mn>100</mn><mo>+</mo><mn>7</mn><mo>=</mo><mn>7</mn></math>. Subtracting <math alttext=\"7\"><mn>7</mn>\n</math> from both sides of this equation yields <math alttext=\"x squared plus 20 x plus 100 equals 0\"><mrow>\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>20</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mn>100</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>. Factoring the left-hand side of this equation yields <math alttext=\"left parenthesis x plus 10 right parenthesis left parenthesis x plus 10 right parenthesis equals 0\"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>10</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>+</mo><mn>10</mn></mrow></mfenced><mo>=</mo><mn>0</mn></math>, or <math alttext=\"left parenthesis x plus 10 right parenthesis squared equals 0\"><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>10</mn></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mn>0</mn></math>. Taking the square root of both sides of this equation yields <math alttext=\"x plus 10 equals 0\"><mrow>\n\t<mrow>\n\t\t<mi>x</mi>\n\t\t<mo>+</mo>\n\t\t<mn>10</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>. Subtracting <math alttext=\"10\"><mn>10</mn>\n</math> from both sides of this equation yields <math alttext=\"x equals negative 10\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mo>-</mo><mn>10</mn>\n</mrow>\n</math>. Therefore, the value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"negative 10\"><mo>-</mo><mn>10</mn>\n</math>.</p>","correct_answer":["-10"],"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}}