{"id":"cb_question_bank:36ab04e0-1af7-476c-bf73-74787643e803","source_id":"cb_question_bank","source_item_id":"36ab04e0-1af7-476c-bf73-74787643e803","external_id":null,"ibn":"070618-DC","question_id":"fcdf87b7","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":"M","score_band":5,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If the ordered pair x comma y satisfies the system of equations above, what is one possible value of x ?","stimulus":"y equals, x squared, minus 4 x, plus 4, and y equals, 4 minus x","stimulus_html":"<div class=\"stimulus_reference \"><p class=\"standalone_statement style:1 \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/61933f170bf1b0d0b0ffd6c5ec31c63555c3adf67066014ec4af06cfa59c3434\" alt=\"y equals, x squared, minus 4 x, plus 4, and y equals, 4 minus x\"></span></span></p></div>\n","stem_html":"<p class=\"stem_paragraph \">If the ordered pair <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/057e200d3c63fad8e09cdb26b2c6eba6928070fc357775850da3c008e193a433\" alt=\"x comma y\"></span></span> satisfies the system of equations above, what is one possible value of <span class=\"italic\">x</span> ?</p>\n","rationale_html":"<p class=\"direction_paragraph \">The correct answer is either 0 or 3. For an ordered pair to satisfy a system of equations, both the <span class=\"italic\">x</span>- and <span class=\"italic\">y</span>-values of the ordered pair must satisfy each equation in the system. Both expressions on the right-hand side of the given equations are equal to <span class=\"italic\">y</span>, therefore it follows that both expressions on the right-hand side of the equations are equal to each other: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/11264bbdfabc9c4a31a9b0059cb208a3a3bd4ae4d54afc1f248b452c722d24d3\" alt=\"x squared, minus 4 x, plus 4, equals, 4 minus x\"></span>. This equation can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/325f0d04ae01fa70f9efc32ac6a7b21028763d22d49d0eeb03ee9e8bf9622640\" alt=\"x squared, minus 3 x, equals 0\"></span>, and then through factoring, the equation becomes <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8eb0eb661e448ec00cca02589759f1f410d3ba41f8b875de33891974b05f1746\" alt=\"x times, open parenthesis, x minus 3, close parenthesis, equals 0\"></span>. Because the product of the two factors is equal to 0, it can be concluded that either <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/37b98ea685bc6992d8e8e7df92ac8c58c1621b437bc601cc6767a21168bc15e0\" alt=\"x equals 0\"></span> or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c619e0ffb3ec741f7160c4024a8e0a02159f87faacdf8309523c55067b7587b3\" alt=\"x minus 3, equals 0\"></span>, or rather, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/37b98ea685bc6992d8e8e7df92ac8c58c1621b437bc601cc6767a21168bc15e0\" alt=\"x equals 0\"></span> or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ceba1165e53a8baa1cf03f75cde85da34750b8ab2728ef25385d77f80f8276c5\" alt=\"x equals 3\"></span>. Note that 0 and 3 are examples of ways to enter a correct answer.</p>\n","correct_answer":["0","3"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.631000+00:00","source_updated_at":"2023-08-02T20:25:59.631000+00:00","options":[],"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}}