{"id":"cb_question_bank:aaf9b597-1021-4b4e-8e95-682707f02e91","source_id":"cb_question_bank","source_item_id":"aaf9b597-1021-4b4e-8e95-682707f02e91","external_id":null,"ibn":"035714-DC","question_id":"0980fcdd","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":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A solution to the given system of equations is the ordered pair x comma y . Which of the following is a possible value of xy ?","stimulus":"Equation 1: x squared equals, 6 x plus y. Equation 2: y equals, negative 6 x, plus 36.","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/19325702bb278243329ad57b2bb78d41b5f2ba27595a1c30ad1fec5d4733e20f\" alt=\"Equation 1: x squared equals, 6 x plus y. \nEquation 2: y equals, negative 6 x, plus 36.\n\"></span></p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">A solution to the given system of equations is <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/338db7e3a31d3afebe84d6ca556e60cbe33b3baf49002acc912917c4ff25d31e\" alt=\"the ordered pair x comma y\"></span></span>. Which of the following is a possible value&nbsp;of&nbsp;<span class=\"italic\">xy</span>&nbsp;?</p>\n","rationale_html":"<p>Choice A is correct. Solutions to the given system of equations are ordered pairs <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/338db7e3a31d3afebe84d6ca556e60cbe33b3baf49002acc912917c4ff25d31e\" alt=\"x comma y \"></span> that satisfy both equations in the system. Adding the left-hand and right-hand sides of the equations in the system yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8274d7d989b1eb8542c689f5f3b7671211ea16e686205b32d414fcd72b1bf37e\" alt=\"x squared, plus y, equals, 6 x plus negative 6 x, plus y, plus 36\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/35662ecd90da87c5c298d42214a987e44ba699eb589d5c77dffbd9a752da4652\" alt=\"x squared, plus y, equals, y plus 36\"></span>. Subtracting <span class=\"italic\">y</span> from both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f7bdea77e0c42da8aaf0eeee85f0f71a097d184696209ff24ff0c9947fc229e9\" alt=\"x squared equals 36\"></span>. Taking the square root of both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4b1023e15d50cb679a3c030c38974bb902514afa9f233eff14c3d4466e78ba4d\" alt=\"x equals 6 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7f945e941c46292c9cc0d455e6bbdffbf446742ab36ebc2042de1937117479ee\" alt=\"x equals negative 6\"></span>. Therefore, there are two solutions to this system of equations, one with an <span class=\"italic\">x</span>-coordinate of 6 and the other with an <span class=\"italic\">x</span>-coordinate of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f8ac4e862b233acbee95c501658ff49dd21661d2a931c76a597fe7d20c5d70df\" alt=\"negative 6\"></span>. Substituting 6 for <span class=\"italic\">x</span> in the second equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b2f4475edc73ea00b84e56f26596040ebea1e7d6e3db14a692845b3c38d384b2\" alt=\"y equals, negative 6 times 6, plus 36\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ce672c12451ce6d730167e9763ac3e67a5ed07d54cba747ed2f59adb20d5d205\" alt=\"y equals 0\"></span>; therefore, one solution is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/92da2a0678a350edea1acf065e8611b933e291685b1114bf6e048d3515e8381c\" alt=\"the ordered pair 6 comma 0\"></span>. Similarly, substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f8ac4e862b233acbee95c501658ff49dd21661d2a931c76a597fe7d20c5d70df\" alt=\"negative 6\"></span> for <span class=\"italic\">x</span> in the second equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9dd82fe904081cc95b0212659c5c1858007234aa9e5d0deac91daf7823fbd5c2\" alt=\"y equals, negative 6 times negative 6, plus 36\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/679628bf43d60c5f45c80f1bf62ee643c7d380c84d1690def5ff2c19742f7508\" alt=\"y equals 72\"></span>; therefore, the other solution is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/817d8690bd61479fc3c6439f9f6cf355047e73638fc42b5ffeab1a5670a9dfb0\" alt=\"the ordered pair negative 6 comma 72\"></span>. It follows then that 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, then possible values of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/64f9e59583537efe7620d310c1e97e050c5aa36dd3e0b74fcc8c3a1c0f301dce\" alt=\"x y   \"></span> are <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a35d86f59d4f54cc8e1329bc568adeba023fb05b7081b6ae1d80e8d3798cbe3f\" alt=\"6 times 0, equals 0\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1cee495ee2c99d4ea2b9119a9a7194830381711d47efd3c06ce57c9f1fb0323d\" alt=\"negative 6 times 72, equals negative 432\"></span>. Only 0 is among the given choices.</p><p>Choice B is incorrect. This is the <span class=\"italic\">x</span>-coordinate of one of the solutions, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/92da2a0678a350edea1acf065e8611b933e291685b1114bf6e048d3515e8381c\" alt=\"the ordered pair 6 comma 0\"></span>. Choice C is incorrect and may result from conceptual or computational errors. Choice D is incorrect. This is the square of the <span class=\"italic\">x</span>-coordinate of one of the solutions, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/92da2a0678a350edea1acf065e8611b933e291685b1114bf6e048d3515e8381c\" alt=\"the ordered pair 6 comma 0\"></span>.</p><p></p>\n","correct_answer":["A"],"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 block_choice\">0</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph block_choice\">6</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph block_choice\">12</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph block_choice\">36</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}}