{"id":"cb_question_bank:6aa421ae-9aa7-40b6-9478-e539b4efc7d7","source_id":"cb_question_bank","source_item_id":"6aa421ae-9aa7-40b6-9478-e539b4efc7d7","external_id":"2afd7270-62a5-4b7b-9b32-31529be1acdd","ibn":null,"question_id":"9db5b5c1","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":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"4 x equals 20 minus 3 x plus y equals negative 7 The solution to the given system of equations is left parenthesis x comma y right parenthesis . What is the value of x plus y ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"4 x equals 20\"><mrow>\n\t<mrow>\n\t\t<mn>4</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>20</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: center;\"><math alttext=\"minus 3 x plus y equals negative 7\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mo>-</mo>\n\t\t\t<mn>3</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<mo>-</mo><mn>7</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 plus y\"><mrow>\n\t<mi>x</mi>\n\t<mo>+</mo>\n\t<mi>y</mi>\n</mrow>\n</math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. It's given that <math alttext=\"4 x equals 20\"><mrow>\n\t<mrow>\n\t\t<mn>4</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>20</mn>\n</mrow>\n</math> and <math alttext=\"minus 3 x plus y equals negative 7\"><mrow>\n\t<mrow>\n\t\t<mrow>\n\t\t\t<mo>-</mo>\n\t\t\t<mn>3</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<mo>-</mo><mn>7</mn>\n</mrow>\n</math> is a system of equations with a solution <math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math>. Adding the second equation in the given system to the first equation yields <math alttext=\"4 x plus left parenthesis minus 3 x plus y right parenthesis equals 20 plus left parenthesis negative 7 right parenthesis\"><mn>4</mn><mi>x</mi><mo>+</mo><mo>(</mo><mo>-</mo><mn>3</mn><mi>x</mi><mo>+</mo><mi>y</mi><mo>)</mo><mo>=</mo><mn>20</mn><mo>+</mo><mfenced><mrow><mo>-</mo><mn>7</mn></mrow></mfenced></math>, which is equivalent to <math alttext=\"x plus y equals 13\"><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>13</mn></math>. Thus, the value of <math alttext=\"x plus y\"><mi>x</mi><mo>+</mo><mi>y</mi></math> is <math alttext=\"13\"><mn>13</mn>\n</math>.&nbsp;</p>\n<p style=\"text-align: left;\">Choice A is incorrect. This represents the value of <math alttext=\"minus 2 left parenthesis x plus y right parenthesis minus 1\"><mo>-</mo><mn>2</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfenced><mo>-</mo><mn>1</mn></math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This represents the value of <math alttext=\"minus left parenthesis x plus y right parenthesis\"><mo>-</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfenced></math>.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This represents the value of <math alttext=\"2 left parenthesis x plus y right parenthesis plus 1\"><mn>2</mn><mfenced><mrow><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfenced><mo>+</mo><mn>1</mn></math>.</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 27\"><mo>-</mo><mn>27</mn>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"negative 13\"><mo>-</mo><mn>13</mn>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"13\"><mn>13</mn>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"27\"><mn>27</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}}