{"id":"cb_question_bank:78c23784-3699-4e6c-8f94-34f6e0f01d23","source_id":"cb_question_bank","source_item_id":"78c23784-3699-4e6c-8f94-34f6e0f01d23","external_id":"648f6724-1596-45f8-99c7-238a1a0648f9","ibn":null,"question_id":"ca9bb527","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"y equals 4 x minus 9 y equals 19 What is the solution left parenthesis x comma y right parenthesis to the given system of equations?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"y equals 4 x minus 9\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>4</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>-</mo>\n\t\t<mn>9</mn>\n\t</mrow>\n</mrow>\n</math><br><math alttext=\"y equals 19\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mn>19</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: left;\">What is the solution <math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math>&nbsp;to the given system of equations?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. It's given by the second equation in the system that <math alttext=\"y equals 19\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mn>19</mn>\n</mrow>\n</math>. Substituting <math alttext=\"19\"><mn>19</mn>\n</math> for <math alttext=\"y\"><mi>y</mi>\n</math> in the first equation yields <math alttext=\"19 equals 4 x minus 9\"><mrow>\n\t<mn>19</mn>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>4</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>-</mo>\n\t\t<mn>9</mn>\n\t</mrow>\n</mrow>\n</math>. Adding <math alttext=\"9\"><mn>9</mn>\n</math> to both sides of this equation yields <math alttext=\"28 equals 4 x\"><mrow>\n\t<mn>28</mn>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>4</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n</mrow>\n</math>. Dividing both sides of this equation by <math alttext=\"4\"><mn>4</mn>\n</math> yields <math alttext=\"7 equals x\"><mrow>\n\t<mn>7</mn>\n\t<mo>=</mo>\n\t<mi>x</mi>\n</mrow>\n</math>. Therefore, since <math alttext=\"x equals 7\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>7</mn>\n</mrow>\n</math> and <math alttext=\"y equals 19\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mn>19</mn>\n</mrow>\n</math>, the solution <math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math> to the given system of equations is <math alttext=\"left parenthesis 7 comma 19 right parenthesis\"><mfenced><mrow><mn>7</mn><mo>,</mo><mn>19</mn></mrow></mfenced></math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.818000+00:00","source_updated_at":"2023-08-02T20:25:59.818000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"left parenthesis 4 comma 19 right parenthesis\"><mfenced><mrow><mrow><mn>4</mn></mrow><mo>,</mo><mrow><mn>19</mn></mrow></mrow></mfenced></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"left parenthesis 7 comma 19 right parenthesis\"><mfenced><mrow><mrow><mn>7</mn></mrow><mo>,</mo><mrow><mn>19</mn></mrow></mrow></mfenced></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"left parenthesis 19 comma 4 right parenthesis\"><mfenced><mrow><mrow><mn>19</mn></mrow><mo>,</mo><mrow><mn>4</mn></mrow></mrow></mfenced></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"left parenthesis 19 comma 7 right parenthesis\"><mfenced><mrow><mrow><mn>19</mn></mrow><mo>,</mo><mrow><mn>7</mn></mrow></mrow></mfenced></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}}