{"id":"cb_question_bank:a2c7bbe5-59af-47b9-8fd5-6e639440d29f","source_id":"cb_question_bank","source_item_id":"a2c7bbe5-59af-47b9-8fd5-6e639440d29f","external_id":"05f30aab-94fb-4835-aaaf-c316bafa965e","ibn":null,"question_id":"2875ba81","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":"6 x plus 7 y equals 28 2 x plus 2 y equals 10 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=\"6 x plus 7 y equals 28\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>6</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mrow>\n\t\t\t<mn>7</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>28</mn>\n</mrow>\n</math><br><math alttext=\"2 x plus 2 y equals 10\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>2</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mrow>\n\t\t\t<mn>2</mn>\n\t\t\t<mi>y</mi>\n\t\t</mrow>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>10</mn>\n</mrow>\n</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 <em>y</em>?</p>","rationale_html":"<p>Choice A is correct. The given system of linear equations can be solved by the elimination method. Multiplying each side of the second equation in the given system by <math alttext=\"3\"><mn>3</mn>\n</math> yields <math alttext=\"left parenthesis 2 x plus 2 y right parenthesis left parenthesis 3 right parenthesis equals left parenthesis 10 right parenthesis left parenthesis 3 right parenthesis\"><mfenced><mrow><mn>2</mn><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mo>(</mo><mn>3</mn><mo>)</mo><mo>=</mo><mfenced><mn>10</mn></mfenced><mfenced><mn>3</mn></mfenced></math>, or <math alttext=\"6 x plus 6 y equals 30\"><mn>6</mn><mi>x</mi><mo>+</mo><mn>6</mn><mi>y</mi><mo>=</mo><mn>30</mn></math>. Subtracting this equation from the first equation in the given system yields <math alttext=\"left parenthesis 6 x plus 7 y right parenthesis minus left parenthesis 6 x plus 6 y right parenthesis equals left parenthesis 28 right parenthesis minus left parenthesis 30 right parenthesis\"><mfenced><mrow><mn>6</mn><mi>x</mi><mo>+</mo><mn>7</mn><mi>y</mi></mrow></mfenced><mo>-</mo><mfenced><mrow><mn>6</mn><mi>x</mi><mo>+</mo><mn>6</mn><mi>y</mi></mrow></mfenced><mo>=</mo><mfenced><mn>28</mn></mfenced><mo>-</mo><mfenced><mn>30</mn></mfenced></math>, which is equivalent to&nbsp;<math alttext=\"left parenthesis 6 x minus 6 x right parenthesis plus left parenthesis 7 y minus 6 y right parenthesis equals 28 minus 30\"><mfenced><mrow><mn>6</mn><mi>x</mi><mo>-</mo><mn>6</mn><mi>x</mi></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>7</mn><mi>y</mi><mo>-</mo><mn>6</mn><mi>y</mi></mrow></mfenced><mo>=</mo><mn>28</mn><mo>-</mo><mn>30</mn></math>, or <math alttext=\"y equals negative 2\"><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn></math>.&nbsp;</p>\n<p>Choice B is incorrect. This is the value of <math alttext=\"x\"><mi>x</mi>\n</math>, not the value of <math alttext=\"y\"><mi>y</mi>\n</math>.</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.</p>\n<p>&nbsp;</p>","correct_answer":["A"],"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=\"negative 2\"><mo>-</mo><mn>2</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"7\"><mn>7</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"14\"><mn>14</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"18\"><mn>18</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}}