{"id":"cb_question_bank:03c3cdb9-a83e-4ba5-b117-81835f5be948","source_id":"cb_question_bank","source_item_id":"03c3cdb9-a83e-4ba5-b117-81835f5be948","external_id":null,"ibn":"10551-DC","question_id":"cb8f449f","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear 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":"The system of equations above has solution ( x , y ). What is the value of x ?","stimulus":"one half y equals 4 x minus, one half y, equals 2","stimulus_html":"<div class=\"stimulus_reference \">\n\t<table class=\"table_Borderless\"><tbody><tr><td class=\"para_right tcp-5d4d032a-0e39-4647-bdb7-a6d885ca8ce5\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8da03c0e6e2bc35e40a38ccb20d751031d16a6d4b182620fb41d812cd79dc66d\" alt=\"one half y equals 4\"></span></td>\n\t\t\t</tr><tr><td class=\"para_right tcp-b5f1f72c-60c5-4986-ae97-7e09cfbdfad8\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/573c291d7cea6b925541d1357b4c95e6633edf53af70bf0e93fc00b3214b017e\" alt=\"x minus, one half y, equals 2\"></span></td>\n\t\t\t</tr></tbody></table></div>\n","stem_html":"<p class=\"stem_paragraph \">The system of equations above has solution (<span class=\"italic\">x</span>, <span class=\"italic\">y</span>). What is the value of <span class=\"italic\">x</span> ?</p>\n","rationale_html":"<p>Choice D is correct. Adding the corresponding sides of the two equations eliminates <span class=\"italic\">y</span> and yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4b1023e15d50cb679a3c030c38974bb902514afa9f233eff14c3d4466e78ba4d\" alt=\"x equals 6\"></span>, as shown.</p><p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d08f692ca98bc0a1825774fd12bff9b56a174eeb5e6dd06efce826507fc09956\" alt=\"The equation one half y equals 4, added to the equation x minus one half y, equals 2, gives the equation x plus 0, equals 6\"></span></p><p>If (<span class=\"italic\">x</span>, <span class=\"italic\">y</span>) is a solution to the system, then (<span class=\"italic\">x</span>, <span class=\"italic\">y</span>) satisfies both equations in the system and any equation derived from them. Therefore, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4b1023e15d50cb679a3c030c38974bb902514afa9f233eff14c3d4466e78ba4d\" alt=\"x equals 6\"></span>.</p><p>Choices A, B, and C are incorrect and may be the result of errors when solving the system.</p><p>&nbsp;</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":true,"source_created_at":"2023-08-02T20:25:59.637000+00:00","source_updated_at":"2023-08-02T20:25:59.637000+00:00","options":[{"label":"A","content_html":"<p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b35ae18904fb781bd47e663cf02b992965491e4f50b31194e7d69870143879cd\" alt=\"three\"></span></p><p>&nbsp;</p><p></p>\n","ord":0},{"label":"B","content_html":"<p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9a8079a7f4b7a6b38b587d62b6646541bd4fab0154c40030df93a1e5afc0f7d3\" alt=\"the fraction 7 over 2\"></span></p><p>&nbsp;</p><p></p>\n","ord":1},{"label":"C","content_html":"<p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8bf3fb601176e63eeff4df74d894a4d3ef6f5b84afee5e9254a35c1ddf0f625c\" alt=\"four\"></span></p><p>&nbsp;</p><p></p>\n","ord":2},{"label":"D","content_html":"<p><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3ba1d0c351ba804f1e264fab3db5d1fb3d2696b974be16e1a3b091433eb096d6\" alt=\"six\"></span></p><p>&nbsp;</p><p></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}}