{"id":"cb_question_bank:47548dc0-42b0-4e09-aaca-80db7779a364","source_id":"cb_question_bank","source_item_id":"47548dc0-42b0-4e09-aaca-80db7779a364","external_id":"b992e5d3-e84d-4c00-86c0-75f34b0c6f14","ibn":null,"question_id":"f5929f7a","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"y equals minus one ninth x y equals one half x 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=\"y equals minus one ninth x\"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mrow><mn>9</mn></mrow></mfrac><mi>x</mi></math></p>\n<p style=\"text-align: center;\"><math alttext=\"y equals one half x\"><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn></mrow></mfrac><mi>x</mi></math></p>\n<p style=\"text-align: left;\">The solution to the given system of equations is <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;\">Choice C is correct. It's given by the first equation in the system that <math alttext=\"y equals minus one ninth x\"><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>9</mn></mfrac><mi>x</mi></math>. Substituting&nbsp;<math alttext=\"minus one ninth x\"><mo>-</mo><mfrac><mn>1</mn><mn>9</mn></mfrac><mi>x</mi></math> for <math alttext=\"y\"><mi>y</mi>\n</math> in the second equation in the system yields <math alttext=\"minus one ninth x equals one half x\"><mo>-</mo><mfrac><mn>1</mn><mn>9</mn></mfrac><mi>x</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi>x</mi></math>. Multiplying the left-hand side of this equation by <math alttext=\"two halves\"><mfrac><mn>2</mn><mn>2</mn></mfrac></math> and the right-hand side by&nbsp;<math alttext=\"nine ninths\"><mfrac><mn>9</mn><mn>9</mn></mfrac></math> yields <math alttext=\"minus two eighteenths x equals nine eighteenths x\"><mo>-</mo><mfrac><mn>2</mn><mn>18</mn></mfrac><mi>x</mi><mo>=</mo><mfrac><mn>9</mn><mn>18</mn></mfrac><mi>x</mi></math>. Adding&nbsp;<math alttext=\"two eighteenths x\"><mfrac><mn>2</mn><mn>18</mn></mfrac><mi>x</mi></math> to both sides of this equation yields <math alttext=\"0 equals StartFraction 11 Over 18 EndFraction x\"><mn>0</mn><mo>=</mo><mfrac><mn>11</mn><mn>18</mn></mfrac><mi>x</mi></math>. Multiplying both sides of this equation by <math alttext=\"StartFraction 18 Over 11 EndFraction\"><mfrac><mn>18</mn><mn>11</mn></mfrac></math> yields <math alttext=\"x equals 0\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>0</mn>\n</mrow>\n</math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.&nbsp;</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.&nbsp;</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.&nbsp;</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.817000+00:00","source_updated_at":"2023-08-02T20:25:59.817000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"negative 9\"><mo>-</mo><mn>9</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"negative 7\"><mo>-</mo><mn>7</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"0\"><mn>0</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"2\"><mn>2</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}}