{"id":"cb_question_bank:9efbeae5-8e99-4366-a2a0-ed3555c3a34b","source_id":"cb_question_bank","source_item_id":"9efbeae5-8e99-4366-a2a0-ed3555c3a34b","external_id":null,"ibn":"070619-DC","question_id":"364a2d25","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":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If one solution to the system of equations above is the ordered pair x comma y , what is one possible value of x ?","stimulus":"Equation 1: x plus y equals 17. Equation 2: x y equals 72.","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/f65ac1a239b6dfc590969f90883c86898c884651a9e8990245e6da1af9326407\" alt=\"Equation 1: x plus y equals 17. Equation 2: x y equals 72.\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">If one solution to the system of equations above is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/338db7e3a31d3afebe84d6ca556e60cbe33b3baf49002acc912917c4ff25d31e\" alt=\"the ordered pair x comma y \"></span>, what is one possible value of <span class=\"italic\">x</span> ?</p>\n","rationale_html":"<p>The correct answer is either 8 or 9. The first equation can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cd568621ba695cd315221848c516ab98f1c1c77de75a128e240684c1f0314855\" alt=\"y equals, 17 minus x\"></span>. Substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8ad41a3a3a9565afcbcb4712b5b3ef388a4fb48625d4bcdc4c3765b6f3ee4c6a\" alt=\"17 minus x\"></span> for <span class=\"italic\">y</span> in the second equation gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6d000632892f68f5d63d0b558c9ba01942eb7d22d8a659235e89e75dad766d2c\" alt=\"x times, open parenthesis, 17 minus x, close parenthesis, equals 72\"></span>. By applying the distributive property, this can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/54dc7d5234d8f19ea7b7db94b82d81dff08fd046a654ca957c90d396783cce14\" alt=\"17 x, minus x squared, equals 72\"></span>. Subtracting 72 from both sides of the equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4ff6ddd0b3e40f297b4bfd4376fbfab821ea9b7b48b8b88c2c26187ce090cb7e\" alt=\"x squared, minus 17 x, plus 72, 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/2c2d0135933bab029d030feffd5502b03d07d3632c8c1b6ef99fa5f14cbda65f\" alt=\"open parenthesis, x minus 8, close parenthesis, times, open parenthesis, x minus 9, close parenthesis, equals 0\"></span>. Applying the Zero Product Property, it follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cda12892439178d9f3e5c886375e30087f11aed3759c7828a58f00f8a0e8a033\" alt=\"x minus 8, equals 0\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ea41db745fed7970c11eaae00765598202e0ffe0b3122ca70cb884c70c9c343b\" alt=\"x minus 9, 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/a96e9d385800b7527327e54feec0d311f481505d8d4219d42e8ba89899a239ea\" alt=\"x equals 8\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fe437f3f888b2bfe0b094b84d4459055ca218494163e4be957074be5b508aa76\" alt=\"x equals 9\"></span> respectively. Note that 8 and 9 are examples of ways to enter a correct answer.</p>\n","correct_answer":["8","9"],"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}}