{"id":"cb_question_bank:8c43a925-ce58-4a13-b30b-d4fb5ee91ae2","source_id":"cb_question_bank","source_item_id":"8c43a925-ce58-4a13-b30b-d4fb5ee91ae2","external_id":"a18ef7d1-8bbd-459a-93cc-e4df62df2c1a","ibn":null,"question_id":"092ad67d","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":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"x plus 2 y equals 6 x minus 2 y equals 4 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=\"x plus 2 y equals 6\"><mrow>\n\t<mrow>\n\t\t<mi>x</mi>\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>6</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: center;\"><math alttext=\"x minus 2 y equals 4\"><mrow>\n\t<mrow>\n\t\t<mi>x</mi>\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>4</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 <math alttext=\"x\"><mi>x</mi>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice B is correct. Adding the first equation to the second equation in the given system yields <math alttext=\"left parenthesis x plus 2 y right parenthesis plus left parenthesis x minus 2 y right parenthesis equals 6 plus 4\"><mfenced><mrow><mi>x</mi><mo>+</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mo>+</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mo>=</mo><mn>6</mn><mo>+</mo><mn>4</mn></math>, or&nbsp;<math alttext=\"left parenthesis x plus x right parenthesis plus left parenthesis 2 y minus 2 y right parenthesis equals 10\"><mfenced><mrow><mi>x</mi><mo>+</mo><mi>x</mi></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>2</mn><mi>y</mi><mo>-</mo><mn>2</mn><mi>y</mi></mrow></mfenced><mo>=</mo><mn>10</mn></math>. Combining like terms in this equation yields <math alttext=\"2 x equals 10\"><mn>2</mn><mi>x</mi><mo>=</mo><mn>10</mn></math>. Dividing both sides of this equation by <math alttext=\"2\"><mn>2</mn>\n</math> yields <math alttext=\"x equals 5\"><mrow>\n\t<mi>x</mi>\n\t<mo>=</mo>\n\t<mn>5</mn>\n</mrow>\n</math>. Thus, the value of <math alttext=\"x\"><mi>x</mi>\n</math> is <math alttext=\"5\"><mn>5</mn>\n</math>.</p>\n<p>Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice D is incorrect. This is the value of <math alttext=\"2 x\"><mrow>\n\t<mn>2</mn>\n\t<mi>x</mi>\n</mrow>\n</math>, not <math alttext=\"x\"><mi>x</mi>\n</math>.</p>","correct_answer":["B"],"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=\"2.5\"><mn>2.5</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"5\"><mn>5</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"6\"><mn>6</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"10\"><mn>10</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}}