{"id":"cb_question_bank:7ab595dd-20eb-4e9a-885f-8a738f5d88f6","source_id":"cb_question_bank","source_item_id":"7ab595dd-20eb-4e9a-885f-8a738f5d88f6","external_id":"e8d1c0cc-b06d-4425-92fb-3beba3af4800","ibn":null,"question_id":"adb0c96c","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear 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":"24 x plus y equals 48 6 x plus y equals 72 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=\"24 x plus y equals 48\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mn>24</mn>\n\t\t\t<mi>x</mi>\n\t\t</mrow>\n\t\t<mo>+</mo>\n\t\t<mi>y</mi>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>48</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: center;\"><math alttext=\"6 x plus y equals 72\"><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<mi>y</mi>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>72</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\"><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></math>. What is the value of <math alttext=\"y\"><mi>y</mi>\n</math>?</p>","rationale_html":"<p>The correct answer is <math alttext=\"80\"><mn>80</mn>\n</math>. Subtracting the second equation in the given system from the first equation yields <math alttext=\"left parenthesis 24 x plus y right parenthesis minus left parenthesis 6 x plus y right parenthesis equals 48 minus 72\"><mfenced><mrow><mn>24</mn><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfenced><mo>-</mo><mfenced><mrow><mn>6</mn><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfenced><mo>=</mo><mn>48</mn><mo>-</mo><mn>72</mn></math>, which is equivalent to&nbsp;<math alttext=\"24 x minus 6 x plus y minus y equals negative 24\"><mn>24</mn><mi>x</mi><mo>-</mo><mn>6</mn><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>24</mn></math>, or&nbsp;<math alttext=\"18 x equals negative 24\"><mn>18</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>24</mn></math>. Dividing each side of this equation by <math alttext=\"3\"><mn>3</mn>\n</math> yields <math alttext=\"6 x equals negative 8\"><mn>6</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>8</mn></math>. Substituting <math alttext=\"negative 8\"><mo>-</mo><mn>8</mn>\n</math> for <math alttext=\"6 x\"><mrow>\n\t<mn>6</mn>\n\t<mi>x</mi>\n</mrow>\n</math> in the second equation yields&nbsp;<math alttext=\"negative 8 plus y equals 72\"><mo>-</mo><mn>8</mn><mo>+</mo><mi>y</mi><mo>=</mo><mn>72</mn></math>. Adding <math alttext=\"8\"><mn>8</mn>\n</math> to both sides of this equation yields <math alttext=\"y equals 80\"><mi>y</mi><mo>=</mo><mn>80</mn></math>.&nbsp;</p>\n<p>Alternate approach: Multiplying each side of the second equation in the given system by <math alttext=\"4\"><mn>4</mn>\n</math> yields <math alttext=\"24 x plus 4 y equals 288\"><mn>24</mn><mi>x</mi><mo>+</mo><mn>4</mn><mi>y</mi><mo>=</mo><mn>288</mn></math>. Subtracting the first equation in the given system from this equation yields&nbsp;<math alttext=\"left parenthesis 24 x plus 4 y right parenthesis minus left parenthesis 24 x plus y right parenthesis equals 288 minus 48\"><mfenced><mrow><mn>24</mn><mi>x</mi><mo>+</mo><mn>4</mn><mi>y</mi></mrow></mfenced><mo>-</mo><mfenced><mrow><mn>24</mn><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfenced><mo>=</mo><mn>288</mn><mo>-</mo><mn>48</mn></math>, which is equivalent to&nbsp;<math alttext=\"24 x minus 24 x plus 4 y minus y equals 240\"><mn>24</mn><mi>x</mi><mo>-</mo><mn>24</mn><mi>x</mi><mo>+</mo><mn>4</mn><mi>y</mi><mo>-</mo><mi>y</mi><mo>=</mo><mn>240</mn></math>, or&nbsp;<math alttext=\"3 y equals 240\"><mn>3</mn><mi>y</mi><mo>=</mo><mn>240</mn></math>. Dividing each side of this equation by <math alttext=\"3\"><mn>3</mn>\n</math> yields&nbsp;<math alttext=\"y equals 80\"><mi>y</mi><mo>=</mo><mn>80</mn></math>.</p>","correct_answer":["80"],"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":[],"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}}