{"id":"cb_question_bank:93abe965-a6f6-47d4-bd01-6a90dafa0dc2","source_id":"cb_question_bank","source_item_id":"93abe965-a6f6-47d4-bd01-6a90dafa0dc2","external_id":"680ee560-0171-401e-8a31-87727153a417","ibn":null,"question_id":"f88970cc","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":"x equals 5 y equals x minus 8 Which of the following points left parenthesis x comma y right parenthesis is the solution to the given system of equations in the xy -plane?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"x equals 5\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>5</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: center;\"><math alttext=\"y equals x minus 8\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mi>x</mi>\n\t\t<mo>-</mo>\n\t\t<mn>8</mn>\n\t</mrow>\n</mrow>\n</math></p>\n<p>Which of the following points <math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math> is the solution to the given system of equations in the <em>xy</em>-plane?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. A solution to a system of equations in the <em>xy</em>-plane is a point&nbsp;<math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math> that lies on the graph of each equation in the system. The first equation given is <math alttext=\"x equals 5\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>5</mn>\n</mrow>\n</math>. Substituting <math alttext=\"5\"><mn>5</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the second given equation yields <math alttext=\"y equals 5 minus 8\"><mi>y</mi><mo>=</mo><mn>5</mn><mo>-</mo><mn>8</mn></math>, or <math alttext=\"y equals negative 3\"><mrow>\n\t<mi>y</mi>\n\t<mo>=</mo>\n\t<mo>-</mo><mn>3</mn>\n</mrow>\n</math>. It follows that in the <em>xy</em>-plane, the point&nbsp;<math alttext=\"left parenthesis 5 comma negative 3 right parenthesis\"><mfenced><mrow><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced></math> lies on the graph of each equation in the system. Therefore, the solution to the given system of equations in the <em>xy</em>-plane is <math alttext=\"left parenthesis 5 comma negative 3 right parenthesis\"><mfenced><mrow><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced></math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect. The point&nbsp;<math alttext=\"left parenthesis 0 comma 0 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math> doesn't lie on the graph of either equation in the given system.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. The point <math alttext=\"left parenthesis 5 comma negative 8 right parenthesis\"><mfenced><mrow><mn>5</mn><mo>,</mo><mo>-</mo><mn>8</mn></mrow></mfenced></math> doesn't lie on the graph of the second equation in the given system.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. The point&nbsp;<math alttext=\"left parenthesis 5 comma 8 right parenthesis\"><mfenced><mrow><mn>5</mn><mo>,</mo><mn>8</mn></mrow></mfenced></math> doesn't lie on the graph of the second equation in the given system.</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 0 comma 0 right parenthesis\"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"left parenthesis 5 comma negative 3 right parenthesis\"><mfenced><mrow><mrow><mn>5</mn></mrow><mo>,</mo><mrow><mo>-</mo><mn>3</mn></mrow></mrow></mfenced></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"left parenthesis 5 comma negative 8 right parenthesis\"><mfenced><mrow><mrow><mn>5</mn></mrow><mo>,</mo><mrow><mo>-</mo><mn>8</mn></mrow></mrow></mfenced></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"left parenthesis 5 comma 8 right parenthesis\"><mfenced><mrow><mrow><mn>5</mn></mrow><mo>,</mo><mrow><mn>8</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}}