{"id":"cb_question_bank:4f264c47-2821-4cc0-9a99-3a29884f5a5b","source_id":"cb_question_bank","source_item_id":"4f264c47-2821-4cc0-9a99-3a29884f5a5b","external_id":null,"ibn":"027122-DC","question_id":"8abed0fb","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":1,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"What is the solution the ordered pair, x comma y, to the given system of equations?","stimulus":"Equation 1: y equals 2 x plus 3. Equation 2: x equals 1.","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ca2ab794816d9f90cf79f9805d448edd174b1949de27eb97b775939d3f990344\" alt=\"Equation 1: y equals 2 x plus 3. Equation 2: x equals 1.\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">What is the solution <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/338db7e3a31d3afebe84d6ca556e60cbe33b3baf49002acc912917c4ff25d31e\" alt=\"the ordered pair, x comma y, \"></span> to the given system of equations?</p>\n","rationale_html":"<p>Choice B is correct. Since it’s given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e4319fe2c5755fc5aa3f69e1a43b989d061cbb17c450f24b51a6616f131de4b\" alt=\"x equals 1\"></span>, substituting 1 for <span class=\"italic\">x</span> in the first equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a520044973547a1d9ea7b5d70cda01bfc9f83bd69f36804cbab630368d5c0a51\" alt=\"y equals, 2 times 1, plus 3\"></span>. Simplifying the right-hand side of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0d25111394ae0b2b65bb7b10868b8fb33b643d08d174788f42c8d225e57d5230\" alt=\"y equals, 2 plus 3\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9f82c1a6f2626e5235d495170f4c7f7c58a2498e80346cd72371855d50bcd092\" alt=\"y equals 5\"></span>. Therefore, the ordered pair <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/401013dcc8a9963a15648d9e44fc062687dcaec6e45345b4d5e765e2a239cb9a\" alt=\"1 comma 5 \"></span> is a solution to the given system of equations.</p><p>Choice A is incorrect and may result from a calculation error when substituting 1 for <span class=\"italic\">x</span> in the first equation. Choices C and D are incorrect. Because it’s given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e4319fe2c5755fc5aa3f69e1a43b989d061cbb17c450f24b51a6616f131de4b\" alt=\"x equals 1\"></span>, <span class=\"italic\">x</span> cannot equal 2 as stated in these ordered pairs.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.621000+00:00","source_updated_at":"2023-08-02T20:25:59.621000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5120bb2010ab11f6b4ed0bdc3b293336721cc0e8241402e080f2c5eac3303c23\" alt=\"1 comma 2\"></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/401013dcc8a9963a15648d9e44fc062687dcaec6e45345b4d5e765e2a239cb9a\" alt=\"1 comma 5\"></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/363e48748cb197dad493adc9e8061cc0a503ad60bd216c5862e3e4fefc7ed096\" alt=\"2 comma 3\"></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9f08840dcab4713bd2649337477ee7c319e65e3c80f7c39d7bf56f1305c13134\" alt=\"2 comma 7\"></span></p>\n","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}}