{"id":"cb_question_bank:03422a73-15ea-4c0a-b655-c48c93adbcf6","source_id":"cb_question_bank","source_item_id":"03422a73-15ea-4c0a-b655-c48c93adbcf6","external_id":null,"ibn":"070615-DC","question_id":"d1b66ae6","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"H","score_band":6,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If the ordered pair x comma y satisfies the system of equations above, what is the value of y ?","stimulus":"negative x plus y, equals negative 3 point 5, and, x plus 3 y, equals 9 point 5","stimulus_html":"<div class=\"stimulus_reference \"><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/b60cd02a3fde4a39a3a26bd052ed5f5267b037a7c6f05216d416592bc8e236eb\" alt=\"negative x plus y, equals negative 3 point 5, and, x plus 3 y, equals 9 point 5\"></span></span></p></div>\n","stem_html":"<p class=\"stem_paragraph \">If <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ced1a64e45813097b535382f249bf54ff204f9e5fa6c7c433d61d47dac6447b2\" alt=\"the ordered pair x comma y\"></span> satisfies the system of equations above, what is the value of <span class=\"italic\">y</span> ?</p>\n","rationale_html":"<p>The correct answer is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/544c1fbf41c46eecd241e072f3fef539763dd2bbcf0350489f405f9d1fa52c78\" alt=\"three halves\"></span>. One method for solving the system of equations for <span class=\"italic\">y</span> is to add corresponding sides of the two equations. Adding the left-hand sides gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/460533171bf549a20c7ca4928dc789e3a0b676cdbd381e89a106b8f4b7c68723\" alt=\"open parenthesis, negative x plus y, close parenthesis, plus, open parenthesis, x plus 3 y, close parenthesis\"></span>, or 4<span class=\"italic\">y</span>. Adding the right-hand sides yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3c9c559eaed72aa8b2f54de3a982da00d44e40c25ad48d90aaea33eae05637cc\" alt=\"negative 3 point 5 plus 9 point 5, equals 6\"></span>. It follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bbbf23a5249e20a27a320d4a0f57f34fbc2c9dafc16539ca37abd6ed3e7522b3\" alt=\"4 y equals 6\"></span>. Finally, dividing both sides of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bbbf23a5249e20a27a320d4a0f57f34fbc2c9dafc16539ca37abd6ed3e7522b3\" alt=\"4 y equals 6\"></span> by 4 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d06c6f86c4443f8389d0bb6a9e556d6ef45d5151354bc08dcffb2702c5e9af42\" alt=\"y equals six fourths\"></span> or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/544c1fbf41c46eecd241e072f3fef539763dd2bbcf0350489f405f9d1fa52c78\" alt=\"three halves\"></span>. Note that 3/2 and 1.5 are examples of ways to enter a correct answer.</p><div id=\"level-access-access-assistant-highlight-container\">&nbsp;</div><p></p>\n","correct_answer":["3/2"],"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}}