{"id":"cb_question_bank:5af44444-11dc-4839-a265-67aabb0d15ad","source_id":"cb_question_bank","source_item_id":"5af44444-11dc-4839-a265-67aabb0d15ad","external_id":null,"ibn":"14931-DC","question_id":"19fdf387","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":"In the xy -plane, the graph of y equals, x plus 3 intersects the graph of y equals, 2 x minus 6 at the point with coordinates a, comma b . What is the value of a ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">In the <span class=\"italic \">xy</span>-plane, the graph of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/43a63d77038494f0ee3dbec46c868a194336f1e786522d14d7acc417b252cb86\" alt=\"y equals, x plus 3 \"></span></span> intersects the graph of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8265f5771c439dc673cdd89a40d8608b71860eb2224a8abd878da108b9ff3403\" alt=\"y equals, 2 x minus 6\"></span></span> at the point <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a7438d2fd6d3cd4feef783fa625560d22e6e8048ef5358ea151bcda055a6b74a\" alt=\"with coordinates a, comma b\"></span></span>. What is the value of <span class=\"italic\">a</span> ?</p>\n","rationale_html":"<p>Choice C is correct. Since the graph of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/43a63d77038494f0ee3dbec46c868a194336f1e786522d14d7acc417b252cb86\" alt=\"y equals, x plus 3 \"></span> intersects the graph of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8265f5771c439dc673cdd89a40d8608b71860eb2224a8abd878da108b9ff3403\" alt=\"y equals, 2 x minus 6\"></span> at the point <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a7438d2fd6d3cd4feef783fa625560d22e6e8048ef5358ea151bcda055a6b74a\" alt=\"with coordinates a, comma b\"></span>, the ordered pair <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a7438d2fd6d3cd4feef783fa625560d22e6e8048ef5358ea151bcda055a6b74a\" alt=\"a, comma b\"></span> is the solution to the system of linear equations consisting of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/43a63d77038494f0ee3dbec46c868a194336f1e786522d14d7acc417b252cb86\" alt=\"y equals, x plus 3 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8265f5771c439dc673cdd89a40d8608b71860eb2224a8abd878da108b9ff3403\" alt=\"y equals, 2 x minus 6\"></span>, and the value of <span class=\"italic\">a</span> is the value of <span class=\"italic\">x</span> in the solution of this system. Since both <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/210c4235c5d6f2007ee90909378c0dd9b57ac9dc70f0cb76918e8ce80a70cc40\" alt=\"x plus 3 \"></span>and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1f6a18f0251b3a0d13e3e998d4eb3187dbf87793108ff73c7daedf0124e0616\" alt=\"2 x minus 6\"></span> are equal to <span class=\"italic\">y</span>, it follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b0f7e5d8fba304a5db6bb55bdbb4cd7cb74544999310b382810d39aa90180ff1\" alt=\"x plus 3, equals, 2 x minus 6\"></span>. Subtracting <span class=\"italic\">x</span> from and adding 6 to both sides of the equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1c09dcf3423c851219c2a8818b80563bd7746f9791414856a661f722cde8d460\" alt=\"9 equals x\"></span>. Therefore, the value of <span class=\"italic\">a </span>is <span class=\"italic\"></span>9<span class=\"italic\">.</span></p><p>Choices A and B are incorrect and may result from a calculation or conceptual error in solving the system of equations consisting of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/43a63d77038494f0ee3dbec46c868a194336f1e786522d14d7acc417b252cb86\" alt=\"y equals, x plus 3 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8265f5771c439dc673cdd89a40d8608b71860eb2224a8abd878da108b9ff3403\" alt=\"y equals, 2 x minus 6\"></span>. Choice D is incorrect. This is the value of <span class=\"italic\">b</span>, not <span class=\"italic\">a</span>.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.639000+00:00","source_updated_at":"2023-08-02T20:25:59.639000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">3</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">6</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">9</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">12</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}}