{"id":"cb_question_bank:ce2a4952-8922-41ac-99a9-1e8a228d83b1","source_id":"cb_question_bank","source_item_id":"ce2a4952-8922-41ac-99a9-1e8a228d83b1","external_id":null,"ibn":"034116-DC","question_id":"567ac7ab","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":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"One of the two equations in a linear system is 2 x plus 6 y, equals 10 . The system has no solution. Which of the following could be the other equation in the system?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">One of the two equations in a linear system is <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f7f70f9b75b2640755263d0b612d267578c21aaa2507ab3d725d01d985168a96\" alt=\"2 x plus 6 y, equals 10\"></span></span>. The system has no solution. Which of the following could be the other equation in the system?</p>\n","rationale_html":"<p>Choice B is correct. A system of two linear equations written in standard form has no solution when the equations are distinct and the ratio of the <span class=\"italic\">x</span>-coefficient to the <span class=\"italic\">y</span>-coefficient for one equation is equivalent to the ratio of the <span class=\"italic\">x</span>-coefficient to the <span class=\"italic\">y</span>-coefficient for the other equation. This ratio for the given equation is 2 to 6, or 1 to 3. Only choice B is an equation that isn’t equivalent to the given equation and whose ratio of the <span class=\"italic\">x</span>-coefficient to the <span class=\"italic\">y</span>-coefficient is 1 to 3.</p><p>Choice A is incorrect. Multiplying each of the terms in this equation by 2 yields an equation that is equivalent to the given equation. This system would have infinitely many solutions. Choices C and D are incorrect. The ratio of the <span class=\"italic\">x</span>-coefficient to the <span class=\"italic\">y</span>-coefficient in <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a5e9829f16e66c715d90f6d1cf06fc45641fa2b5b464fc7308bd68f3bbc0d6c4\" alt=\"6 x minus 2 y, equals 0\"></span> (choice C) is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f8ac4e862b233acbee95c501658ff49dd21661d2a931c76a597fe7d20c5d70df\" alt=\"negative 6\"></span> to 2, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b62558094601a23d6fe95ffbc037ca0c41dd10264b6e51f4163b9ed575c135a3\" alt=\"negative 3 \"></span> to 1. This ratio in <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dbd3d128e908007a5eaa4664e36a6b3501c67a499ad3112106ccb38129680a67\" alt=\"6 x plus 2 y, equals 10 \"></span> (choice D) is 6 to 2, or 3 to 1. Since neither of these ratios is equivalent to that for the given equation, these systems would have exactly one solution.</p><p></p>\n","correct_answer":["B"],"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\">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/78d1aadce9e71dd748f8d924f89c659a3aabbc690c8b3b14c37694a3c026224f\" alt=\"x plus 3 y, equals 5\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph block_choice\">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/41177eaf7fccd400cf0d758dad228d58d595334ec9fb1b2f5099da47fc89e841\" alt=\"x plus 3 y, equals negative 20\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph block_choice\">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/416e45e3a5fd09a573a72e1192c3b83fce8f9dc79f5a554f97fbdadbb896ba46\" alt=\"6 x minus 2 y, equals 0\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph block_choice\">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f58ad5cba81c10d0b941afba07c36620eba2b0f4657e016780c4f281a83aa398\" alt=\"6 x plus 2 y, equals 10 \"></span></span>\n          </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}}