{"id":"cb_question_bank:819e8084-a758-4a17-8699-8cda78e28751","source_id":"cb_question_bank","source_item_id":"819e8084-a758-4a17-8699-8cda78e28751","external_id":null,"ibn":"032680-DC","question_id":"568aaf27","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":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If the ordered pair x comma y is a solution to the system of equations above, which of the following is a possible value of x ?","stimulus":"Equation 1: x plus y equals 12. Equation 2: y equals x squared.","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/2fca2b06777f9333a36d81120022e0ff21243915dd964d56b8f5f9018c0974cb\" alt=\"Equation 1: x plus y equals 12. Equation 2: y equals x squared.\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">If <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/338db7e3a31d3afebe84d6ca556e60cbe33b3baf49002acc912917c4ff25d31e\" alt=\"the ordered pair x comma y\"></span> is a solution to the system of equations above, which of the following is a possible value of <span class=\"italic\">x</span>?</p>\n","rationale_html":"<p>Choice D is correct. Substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3a186314172bc239fb025135d8722d39ee39bfefe4e212836956158aa0b9ff08\" alt=\"x squared \"></span> from the second equation for <span class=\"italic\">y</span> in the first equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a01bf46370190e369ac1973f22aa52fe1878aafea2ea446aa0b3c63613792590\" alt=\"x plus x squared, equals 12\"></span>. Subtracting 12 from both sides of this equation and rewriting the equation results in <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/37dea9f591bdb309c99bfab75b9777a3559e9ad27619415e20cb3752ec506f12\" alt=\"x squared, plus x, minus 12, equals 0\"></span>. Factoring the left-hand side of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/272c6c5e2e98b293ae5ca15248160f69c4e5a640cd4b2fe304f57f183c1a0927\" alt=\"open parenthesis, x minus 3, close parenthesis, times, open parenthesis, x plus 4, close parenthesis, equals 0\"></span>. Using the zero product property to solve for <span class=\"italic\">x</span>, it follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c619e0ffb3ec741f7160c4024a8e0a02159f87faacdf8309523c55067b7587b3\" alt=\"x minus 3, equals 0 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bedc920ad278563ba967e90e271ee5a22a4065511dc66ee9f8d9ff2498d9b88d\" alt=\"x plus 4, equals 0\"></span>. Solving each equation for <span class=\"italic\">x</span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ceba1165e53a8baa1cf03f75cde85da34750b8ab2728ef25385d77f80f8276c5\" alt=\"x equals 3 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b2271bf6a6395b1b35156f1d6b258d0ebf35d2f79134117675d045c2f48b0d63\" alt=\"x equals negative 4\"></span>, respectively. Thus, two possible values of <span class=\"italic\">x</span> are 3 and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bc0609d3d5523eaf8e35097c2a9c872ba31206db61297d0a21597123b1c843d7\" alt=\"negative 4\"></span>. Of the choices given, 3 is the only possible value of <span class=\"italic\">x</span>.</p><p>Choices A, B, and C are incorrect. Substituting 0 for <span class=\"italic\">x</span> in the first equation gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bd5081e62f1c9a48fd645b72168266bbd7b13c3b3c6d0e1abcb5985d1bedd6d6\" alt=\"0 plus y, equals 12\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a4106ab2c6b9b85bbef3b253046f60a8686044d7ca5693622193b3a6c028334a\" alt=\"y equals 12\"></span>; then, substituting 12 for <span class=\"italic\">y</span> and 0 for <span class=\"italic\">x</span> in the second equation gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/92d8b6f8aa931fd29e0106af2090cc554d60a02ce94cacdd86e9367dd846e5d3\" alt=\"12 equals 0 squared\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/019d9fe7ce5e8ec904bcf19a27b6d61d145f0233f031d8d779908d8888b92744\" alt=\"12 equals 0\"></span>, which is false. Similarly, substituting 1 or 2 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/2275134d5a46485bfa03089303d58d5f6d27b0e8fbd57d47b7ecd0de2f6dfd88\" alt=\"y equals 11 \"></span> or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ab2c1069148739a48919a5499bc006554537675f5776686a69f7f87c4d4aaa16\" alt=\"y equals 10\"></span>, respectively; then, substituting 11 or 10 for <span class=\"italic\">y</span> in the second equation yields a false statement.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.627000+00:00","source_updated_at":"2023-08-02T20:25:59.627000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">0</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">1</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">2</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">3</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}}