{"id":"cb_question_bank:a6f0c8eb-e1b1-442c-8e35-226dc6395289","source_id":"cb_question_bank","source_item_id":"a6f0c8eb-e1b1-442c-8e35-226dc6395289","external_id":null,"ibn":"070616-DC","question_id":"466b87e3","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":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"In the system of equations above, c is a constant. If the system has no solution, what is the value of c ?","stimulus":"Equation 1: y equals, one half x, plus 8. Equation 2: y equals, c x plus 10.","stimulus_html":"<div class=\"stimulus_reference \">\n\t\t\t\t<p class=\"standalone_statement style:1 \">\n\t\t\t\t\t<span class=\"math_expression \">\n\t\t\t\t\t\t<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/890f4e91c8172c7c33c24d77856457b11ff69aad1cd3f278f68030f955c3f8b7\" alt=\"Equation 1: y equals, one half x, plus 8. Equation 2: y equals, c x plus 10.\"></span></span>\n\t\t\t\t</p>\n\t\t\t</div>\n","stem_html":"<p class=\"stem_paragraph \">In the system of equations above, <span class=\"italic\">c</span> is a constant. If the system has no solution, what is the value of <span class=\"italic\">c</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/acd304db4db3ee4a427462753769f86b9941b320104a3856da731c39db5d894c\" alt=\"one half\"></span>. A system of two linear equations has no solution when the graphs of the equations have the same slope and different <span class=\"italic\">y</span>-intercepts. Each of the given linear equations is written in the slope-intercept form, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/39dda01984e771026b6a8a741d3ebb66f1a29f1e81583b67f8d50f6e2dbb783e\" alt=\"y equals, m x plus b\"></span>, where <span class=\"italic\">m</span> is the slope and <span class=\"italic\">b</span> is the <span class=\"italic\">y</span>-coordinate of the <span class=\"italic\">y</span>-intercept of the graph of the equation. For these two linear equations, the <span class=\"italic\">y</span>-intercepts are <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c70dad9c5d7e08654895d2f8415c4b119438ee7d30bb486dc23b498db3c51899\" alt=\"the points with coordinates 0 comma 8  \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bb7699ac1a64d36b0d0772c6d1813f2b85746c6d8a086046d2faec1b2a7da208\" alt=\"0 comma 10 \"></span>. Thus, if the system of equations has no solution, the slopes of the graphs of the two linear equations must be the same. The slope of the graph of the first linear equation is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/acd304db4db3ee4a427462753769f86b9941b320104a3856da731c39db5d894c\" alt=\"one half\"></span>. Therefore, for the system of equations to have no solution, the value of <span class=\"italic\">c</span> must be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/acd304db4db3ee4a427462753769f86b9941b320104a3856da731c39db5d894c\" alt=\"one half\"></span>. Note that 1/2 and .5 are examples of ways to enter a correct answer.<span class=\"italic\"></span>\n\t\t\t</p>\n","correct_answer":["1/2"],"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}}