{"id":"cb_question_bank:4f64bfc3-b4c1-416b-bc50-eb86b5faeb0e","source_id":"cb_question_bank","source_item_id":"4f64bfc3-b4c1-416b-bc50-eb86b5faeb0e","external_id":null,"ibn":"026145-DC","question_id":"e1259a5a","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":1,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following points is the solution to the system of equations?","stimulus":"A system of two linear equations is graphed in the xy -plane below. The figure presents the graph of 2 lines in the x y plane. The numbers negative 4 through 16, in increments of 2, are indicated on the x axis. The numbers negative 4 through 20, in increments of 2, are indicated on the y axis. One line begins above the x axis and to the left of the y axis. It moves upward and to the right, crossing the y axis at 6, and passing through the point with coordinates 3 comma 9 and the point with coordinates 12 comma 18. The other line begins below the x axis and to the left of the y axis. It moves upward and to the right, crossing the y axis at 3, and passing through the point with coordinates 3 comma 9 and the point with coordinates 6 comma 15. The two lines intersect at the point with coordinates 3 comma 9.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"passage \">\n          <div class=\"prose style:1 \">\n            <p class=\"passage_para \">A system of two linear equations is graphed in the <span class=\"italic \">xy</span>-plane below.</p>\n            <div class=\"standalone_image \">\n              <img src=\"/api/assets/bc4f9db677f5cd5597395f2cc6a01a8c452995a9dc1c09d0fd01ae1fd80f4c31\" alt=\"The figure presents the graph of 2 lines in the x y plane. The numbers negative 4 through 16, in increments of 2, are indicated on the x axis. The numbers negative 4 through 20, in increments of 2, are indicated on the y axis. One line begins above the x axis and to the left of the y axis. It moves upward and to the right, crossing the y axis at 6, and passing through the point with coordinates 3 comma 9 and the point with coordinates 12 comma 18. The other line begins below the x axis and to the left of the y axis. It moves upward and to the right, crossing the y axis at 3, and passing through the point with coordinates 3 comma 9 and the point with coordinates 6 comma 15. The two lines intersect at the point with coordinates 3 comma 9.\" width=\"198\" height=\"237\"></div>\n          </div>\n        </div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following points is the solution to the system of equations?</p>\n","rationale_html":"<p>Choice A is correct. The solution to this system of linear equations is the point that lies on both lines graphed, or the point of intersection of the two lines. According to the graphs, the point of intersection occurs when <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ceba1165e53a8baa1cf03f75cde85da34750b8ab2728ef25385d77f80f8276c5\" alt=\"x equals 3 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fd065e35eaaa05cd6c85c5d943d89a591bb173a50420363985a49d34a39dfcde\" alt=\"y equals 9\"></span>, or at the point <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ac651bb57bf377aea6eab9dd529447849dd6bbcaa85533907fe7ed09aadc794d\" alt=\"with coordinates 3 comma 9\"></span>.</p><p>Choices B and D are incorrect. Each of these points lies on one line, but not on both lines in the <span class=\"italic\">xy</span>-plane. Choice C is incorrect. This point doesn’t lie on either of the lines graphed in the <span class=\"italic\">xy</span>-plane.</p><p></p>\n","correct_answer":["A"],"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 \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ac651bb57bf377aea6eab9dd529447849dd6bbcaa85533907fe7ed09aadc794d\" alt=\"the point with coordinates 3 comma 9\"></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/35904b2693cb800939283c90167ef9521e604ff974649b2de8896b9c047ad3c9\" alt=\"the point with coordinates 6 comma 15\"></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1c2165cde10792346423c0de41925012857b7367b977b7bead9a3c3dd43a2a94\" alt=\"the point with coordinates 8 comma 10\"></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d8cc613208cb5f31925e1156fd96263435a88cfa602e931e78434c55e42f53c9\" alt=\"the point with coordinates 12 comma 18\"></span></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}}