{"id":"cb_question_bank:c55b23b0-1cb1-4637-a1c6-e710dc6d07b0","source_id":"cb_question_bank","source_item_id":"c55b23b0-1cb1-4637-a1c6-e710dc6d07b0","external_id":null,"ibn":"05314-DC","question_id":"876a731c","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":"If ( x , y ) is a solution of the system of equations above and x > 0, what is the value of xy ?","stimulus":"y equals x squared 2 y plus 6, equals, 2 times, open parenthesis, x plus 3, close parenthesis","stimulus_html":"<div class=\"stimulus_reference \">\n\t<table class=\"table_Borderless\"><tbody><tr><td class=\"para_center tcp-2d44842d-4280-4f9a-a0a3-e9e3d2b9384f\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/faa7a158dbb3661767074b5684bf7109e6511e2993b7a54bd2bdeb1811b22c32\" alt=\"y equals x squared\"></span></td>\n\t\t\t</tr><tr><td class=\"para_center tcp-6955af12-df0e-4388-bd3b-8f1f084d1b32\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c00490b888b280ca81b778cf45550436b59ae34bde6b30a66ab920185e2588e6\" alt=\"2 y plus 6, equals, 2 times, open parenthesis, x plus 3, close\nparenthesis\"></span></td>\n\t\t\t</tr></tbody></table></div>\n","stem_html":"<p class=\"stem_paragraph \">If&nbsp;(<span class=\"italic\">x</span>, <span class=\"italic\">y</span>) is a solution of the system of equations above and <span class=\"italic\">x</span> &gt; 0, what is the value of&nbsp;<span class=\"italic\">xy</span> ?</p>\n","rationale_html":"<p>Choice A is correct. Substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3a186314172bc239fb025135d8722d39ee39bfefe4e212836956158aa0b9ff08\" alt=\"x squared\"></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/80345ebbb493de0dda5a53329efca465901d62968c67dde16308c0ac623a5351\" alt=\"2 times, x squared, plus 6, equals, 2 times, open parenthesis, x plus 3, close parenthesis\"></span>. This equation can be solved as follows:</p><div class=\"tcp-03c15f24-799a-44a2-be34-df400508c3e3\">\n\t<table class=\"table_Borderless tcp-c425e124-3227-4af9-a2c7-652aeb085881\"><tbody><tr><td class=\"tcp-af3a9c03-4eb8-4c37-a5f8-e51ed84f3376\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5601fa7146ff682a357640c27201428b15e199f8d1b4630307d217250baf6fa2\" alt=\"2 x squared, plus 6, equals, 2 x plus 6\"></span></td>\n\t\t\t\t<td class=\"tcp-5ad91201-6479-447c-99f8-e1b070cc9dc9\">Apply the distributive property.</td>\n\t\t\t</tr><tr><td class=\"tcp-7d1d2c42-c52b-455a-aee9-f175160688c0\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ef56e9f80f6364b11c458b6ba4364ab8a85d720ef67b27640169b6d24fe37fc2\" alt=\"2 x squared, plus 6, minus 2 x, minus 6, equals 0\"></span></td>\n\t\t\t\t<td class=\"tcp-9c78c3d0-df94-453c-8065-266e563e9e80\">Subtract 2x and 6 from both sides of the equation.</td>\n\t\t\t</tr><tr><td class=\"tcp-4e7eba3a-196e-4425-9f98-804573042022\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/37b3bef23a8c7b369ff3411c7a1cf5208023d24a88a7c401c83c6e2f09a21504\" alt=\"2 x squared, minus 2 x, equals 0\"></span></td>\n\t\t\t\t<td class=\"tcp-d1031b08-e2ba-45a9-af31-cfb869f1f2ef\">Combine like terms.</td>\n\t\t\t</tr><tr><td class=\"tcp-ef000b74-257c-4399-b576-122afdf9e904\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/564e1a1996e2a3ea4c45da22425cbab743352c01abac17c2b773b0c316482409\" alt=\"2 x times, open parenthesis, x minus 1, close parenthesis, equals 0\"></span></td>\n\t\t\t\t<td class=\"tcp-d4bca920-a349-422d-9047-df707fdc8bc8\">Factor both terms on the left side of the equation<br>\n\t\t\t\t\tby 2x.</td>\n\t\t\t</tr></tbody></table></div><p>Thus, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/37b98ea685bc6992d8e8e7df92ac8c58c1621b437bc601cc6767a21168bc15e0\" alt=\"x equals 0\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e4319fe2c5755fc5aa3f69e1a43b989d061cbb17c450f24b51a6616f131de4b\" alt=\"x equals 1\"></span> are the solutions to the system. Since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6ca09b244cb4a0414885894bc1ac4e0242305210b23d08ccb20204e38d574daf\" alt=\"x is greater than 0\"></span>, only <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e4319fe2c5755fc5aa3f69e1a43b989d061cbb17c450f24b51a6616f131de4b\" alt=\"x equals 1\"></span> needs to be considered. The value of <span class=\"italic\">y</span> when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6e4319fe2c5755fc5aa3f69e1a43b989d061cbb17c450f24b51a6616f131de4b\" alt=\"x equals 1\"></span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3c11b3a831e7307e76b0f243df8fd0261dfa74fbff41c93a03ab7d435a885998\" alt=\"y equals x squared, which equals 1 squared, which equals 1\"></span>. Therefore, the value of <span class=\"italic\">xy</span> is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c81fc1495b834aa065b0bb69f88cd7882c73a7edfd928da12dafbcbba7a42a41\" alt=\"1 times 1, equals 1\"></span>.</p><p>Choices B, C, and D are incorrect and likely result from a computational or conceptual error when solving this system of equations.</p><p>&nbsp;</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":true,"source_created_at":"2023-08-02T20:25:59.628000+00:00","source_updated_at":"2023-08-02T20:25:59.628000+00:00","options":[{"label":"A","content_html":"<p>1</p>\n","ord":0},{"label":"B","content_html":"<p>2</p>\n","ord":1},{"label":"C","content_html":"<p>3</p>\n","ord":2},{"label":"D","content_html":"<p>9</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}}