{"id":"cb_question_bank:b5533c6b-a0ad-46b3-8ca4-f811dce1427e","source_id":"cb_question_bank","source_item_id":"b5533c6b-a0ad-46b3-8ca4-f811dce1427e","external_id":"cd40484a-aae7-48a6-883c-e658d661353a","ibn":null,"question_id":"a67a439d","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of 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":"x plus 7 equals 10 left parenthesis x plus 7 right parenthesis squared equals y Which ordered pair left parenthesis x comma y right parenthesis is a solution to the given system of equations?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: center;\"><math alttext=\"x plus 7 equals 10\"><mrow>\n\t<mrow>\n\t\t<mi>x</mi>\n\t\t<mo>+</mo>\n\t\t<mn>7</mn>\n\t</mrow>\n\t<mo>=</mo>\n\t<mn>10</mn>\n</mrow>\n</math></p>\n<p style=\"text-align: center;\"><math alttext=\"left parenthesis x plus 7 right parenthesis squared equals y\"><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mrow><mn>7</mn></mrow></mrow></mfenced><mn>2</mn></msup><mo>=</mo><mi>y</mi></math></p>\n<p style=\"text-align: left;\">Which ordered pair <math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math> is a solution to the given system of equations?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. The solution to a system of equations is the ordered pair&nbsp;<math alttext=\"left parenthesis x comma y right parenthesis\"><mfenced><mrow><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced></math> that satisfies all equations in the system. It's given by the first equation in the system that <math alttext=\"x plus 7 equals 10\"><mi>x</mi><mo>+</mo><mn>7</mn><mo>=</mo><mn>10</mn></math>. Substituting <math alttext=\"10\"><mn>10</mn>\n</math> for <math alttext=\"x plus 7\"><mrow>\n\t<mi>x</mi>\n\t<mo>+</mo>\n\t<mn>7</mn>\n</mrow>\n</math> into the second equation yields <math alttext=\"10 squared equals y\"><msup><mn>10</mn><mn>2</mn></msup><mo>=</mo><mi>y</mi></math>, or <math alttext=\"y equals 100\"><mi>y</mi><mo>=</mo><mn>100</mn></math>. The <em>x</em>-coordinate of the solution to the system of equations can be found by subtracting <math alttext=\"7\"><mn>7</mn>\n</math> from both sides of the equation <math alttext=\"x plus 7 equals 10\"><mi>x</mi><mo>+</mo><mn>7</mn><mo>=</mo><mn>10</mn></math>, which yields <math alttext=\"x equals 3\"><mi>x</mi><mo>=</mo><mn>3</mn></math>. Therefore, the ordered pair&nbsp;<math alttext=\"left parenthesis 3 comma 100 right parenthesis\"><mfenced><mrow><mn>3</mn><mo>,</mo><mn>100</mn></mrow></mfenced></math> is a solution to the given system of equations.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.823000+00:00","source_updated_at":"2023-08-02T20:25:59.823000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"left parenthesis 3 comma 100 right parenthesis\"><mfenced><mrow><mrow><mn>3</mn></mrow><mo>,</mo><mrow><mn>100</mn></mrow></mrow></mfenced></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"left parenthesis 3 comma 3 right parenthesis\"><mfenced><mrow><mrow><mn>3</mn></mrow><mo>,</mo><mrow><mn>3</mn></mrow></mrow></mfenced></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"left parenthesis 3 comma 10 right parenthesis\"><mfenced><mrow><mrow><mn>3</mn></mrow><mo>,</mo><mrow><mn>10</mn></mrow></mrow></mfenced></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"left parenthesis 3 comma 70 right parenthesis\"><mfenced><mrow><mrow><mn>3</mn></mrow><mo>,</mo><mrow><mn>70</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}}