{"id":"cb_question_bank:05df57bf-69fe-4a7c-9aaa-053ff31a97df","source_id":"cb_question_bank","source_item_id":"05df57bf-69fe-4a7c-9aaa-053ff31a97df","external_id":null,"ibn":"08148-DC","question_id":"d0a7871e","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":4,"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 could be the value of x ?","stimulus":"y equals, x plus 1, and, y equals, x squared plus x","stimulus_html":"<div class=\"stimulus_reference \">\n\t<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/726ee59a78bc93b65504f9a584155af33c98b5e2b709154b73d32c99b6ebf7f4\" alt=\"y equals, x plus 1, \nand,\ny equals, x squared plus x\"></span></span></p>\n</div>\n","stem_html":"<p class=\"stem_paragraph \">If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/29eda5c740cd27d857d88b32b6e6a8a1d263911ac678e319dd0387efa41b0e58\" alt=\"the ordered pair x comma y\"></span></span> is a solution to the system of equations above, which of the following could be the value of <span class=\"italic\">x </span>?</p>\n","rationale_html":"<p>Choice A is correct. It is given that&nbsp;<span class=\"italic\">y</span> = <span class=\"italic\">x</span> + 1 and <span class=\"italic\">y = </span><span class=\"italic\">x</span><sup>2</sup> + <span class=\"italic\">x. </span>Setting the values for <span class=\"italic\">y</span>&nbsp;equal to each other yields&nbsp;<span class=\"italic\">x</span> + 1 = <span class=\"italic\">x<sup>2</sup></span> + <span class=\"italic\">x. S</span>ubtracting <span class=\"italic\">x</span> from each side of this equation yields<span class=\"italic\">&nbsp;x</span><sup>2</sup> = 1. Therefore, <span class=\"italic\">x</span> can equal 1 or –1. Of these, only –1 is given as a choice.</p><p>Choice B is incorrect. If <span class=\"italic\">x</span> = 0, then <span class=\"italic\">x</span> + 1 = 1, but <span class=\"italic\">x</span><sup>2</sup> + <span class=\"italic\">x</span> = 0<sup>2</sup>&nbsp;+ 0 = 0 ≠︀&nbsp;1. Choice C is incorrect. If <span class=\"italic\">x</span> = 2, then <span class=\"italic\">x</span> + 1 = 3, but <span class=\"italic\">x</span><sup>2</sup> + <span class=\"italic\">x</span> = 2<sup>2</sup> + 2 = 6 ≠︀&nbsp;3. Choice D is incorrect. If <span class=\"italic\">x</span> = 3, then <span class=\"italic\">x</span> + 1 = 4, but <span class=\"italic\">x</span><sup>2</sup> + <span class=\"italic\">x</span> = 3<sup>2</sup> + 3 = 12 ≠︀&nbsp;4.</p><p>&nbsp;</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.635000+00:00","source_updated_at":"2023-08-02T20:25:59.635000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">–1</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">0</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}}