{"id":"cb_question_bank:afab2cda-c995-4136-970d-d2ed19e66b78","source_id":"cb_question_bank","source_item_id":"afab2cda-c995-4136-970d-d2ed19e66b78","external_id":null,"ibn":"026034-DC","question_id":"cd33b015","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.D.","skill":"Systems of two linear equations in two variables","difficulty":"E","score_band":2,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"If the ordered pair x comma y is the solution to the given system of equations, what is the value of y ?","stimulus":"Equation 1: x plus y, equals 20. Equation 2: 2 times, open parenthesis, x plus y, close parenthesis, plus 3 y, equals 85.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"passage \">\n          <div class=\"prose style:1 \">\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/2f8d850aeee5202e1c1426900b16064b237138770e25192605342fc4b3ed52fc\" alt=\"Equation 1: x plus y, equals 20. Equation 2: 2 times, open parenthesis, x plus y, close parenthesis, plus 3 y, equals 85.\"></span></span>\n            </p>\n          </div>\n        </div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">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 the solution to the given system of equations, what is the value of <span class=\"italic\">y</span> ?</p>\n","rationale_html":"<p>Choice B is correct. Substituting 20 for <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cda47c0545ab5e31a2a18321fec5f60481bc4b78af6eeb43b47e2fc0085e6be4\" alt=\"x plus y \"></span> in the second equation in the system yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2d2f55848fe9ae101919ae2f1aebcf642094f729c7c444d738a3b396ad1a4058\" alt=\"2 times 20, plus 3y, equals 85\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/576a45501d9a7fc58da588bb5cde1027515094a7df5f7775c6429a9863f65295\" alt=\"40 plus 3 y, equals 85\"></span>. Subtracting 40 from both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ec984f868fbf8d7ca03162c33c218adc68902b2c8f64c373b215c3f40eaadd9b\" alt=\"3 y equals 45\"></span>. Dividing both sides of this equation by 3 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f52c8aa3e5f94ebd1d3f02fb933205f46b8fd0a11c0584851cc5fab3b205ecf3\" alt=\"y equals 15\"></span>.</p><p>Choice A is incorrect. If <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ab2c1069148739a48919a5499bc006554537675f5776686a69f7f87c4d4aaa16\" alt=\"y equals 10\"></span>, then <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8c30fa59b80bc321310bac667bdd8db1351ae6d7d7cc648ba59bf28bd6aefbdd\" alt=\"x equals 10\"></span> since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cd5a9ec3b6e179e2d2a26145de3509988630bd6a8f0b488d83091f9a963f9b5f\" alt=\"x plus y, equals 20\"></span>. However, substituting 10 for both <span class=\"italic\">x</span> and <span class=\"italic\">y</span> in the second equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d23aa4a2090dc044bbedb10153951953d3fd196fa98b6fb9afbf73b0246e6dd9\" alt=\"70 equals 85\"></span>, which is a false statement. Choice C is incorrect. If <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/59850a547362ecc9c5b945fd814f76baa3bfd1b2aaedcc103f7111a0b3a33c2b\" alt=\"y equals 60\"></span>, then <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2eabed7932958ad9d02e7e5a22d5cf8ad61078f0840e2f4393a2fdbb5e6656a7\" alt=\"x equals negative 40 \"></span> since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cd5a9ec3b6e179e2d2a26145de3509988630bd6a8f0b488d83091f9a963f9b5f\" alt=\"x plus y, equals 20\"></span>. However, substituting these values for <span class=\"italic\">x</span> and <span class=\"italic\">y</span> in the second equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/628d287ddac4fa9aa726d43c84d94283e38f2815303fff7876dd67d1078ddf66\" alt=\"220 equals 85\"></span>, which is a false statement. Choice D is incorrect. If <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d067460631a17ae65493e5230639e586c82d91e43ec2bf5cb60dda572a9ad83c\" alt=\"y equals 65\"></span>, then <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fe371cd07e58a691b7d0b29a95a73f5b3cff5325c9482cd338e6ed0c99112bd0\" alt=\"x equals negative 45 \"></span> since <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cd5a9ec3b6e179e2d2a26145de3509988630bd6a8f0b488d83091f9a963f9b5f\" alt=\"x plus y, equals 20\"></span>. However, substituting these values for <span class=\"italic\">x</span> and <span class=\"italic\">y</span> in the second equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e262c5d10d0128aaf371aec26bccbb6ee3717c9fb085d070586a80b9d9dedd2a\" alt=\"235 equals 85\"></span>, which is a false statement.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.620000+00:00","source_updated_at":"2023-08-02T20:25:59.620000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph block_choice\">10</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph block_choice\">15</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph block_choice\">60</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph block_choice\">65</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}}