{"id":"cb_question_bank:04d5b4e8-f3c3-42ad-801b-32f257f2acbf","source_id":"cb_question_bank","source_item_id":"04d5b4e8-f3c3-42ad-801b-32f257f2acbf","external_id":null,"ibn":"026003-DC","question_id":"a5663025","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.B.","skill":"Nonlinear equations in one variable and systems of 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":"A system of equations consists of a quadratic equation and a linear equation. The equations in this system are graphed in the xy -plane above. How many solutions does this system have?","stimulus":"The figure presents the graph of a curve and a line in the x y plane, with the origin labeled O. The numbers negative 10 through 10, in increments of 5, are indicated on each axis. The line begins slightly below the x axis and to the left of the y axis, crosses the x axis at negative 10 and crosses the y axis at approximately 2. It ends above the x axis and to the right of the y axis. The curve is in the shape of a parabola that opens upward and has its vertex at approximately negative 2 point 5 on the y axis. The parabola crosses the x axis at approximately negative 5 and 5. The line and curve intersect at the point with approximate coordinates negative 6 comma 1, and at the point with approximate coordinates 7 comma 4.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"standalone_image \">\n          <img src=\"/api/assets/25820b3e2ec25ed7e289bc91d74087fec601b205f862bf6d670ab8b637161dc7\" alt=\"The figure presents the graph of a curve and a line in the x y plane, with the origin labeled O. The numbers negative 10 through 10, in increments of 5, are indicated on each axis. The line begins slightly below the x axis and to the left of the y axis, crosses the x axis at negative 10 and crosses the y axis at approximately 2. It ends above the x axis and to the right of the y axis. The curve is in the shape of a parabola that opens upward and has its vertex at approximately negative 2 point 5 on the y axis. The parabola crosses the x axis at approximately negative 5 and 5. The line and curve intersect at the point with approximate coordinates negative 6 comma 1, and at the point with approximate coordinates 7 comma 4.\" width=\"127\" height=\"132\"></div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">A system of equations consists of a quadratic equation and a linear equation. The equations in this system are graphed in the <span class=\"italic \">xy</span>-plane above. How many solutions does this system have?</p>\n","rationale_html":"<p>Choice C is correct. The solutions to a system of two equations correspond to points where the graphs of the equations intersect. The given graphs intersect at 2 points; therefore, the system has 2 solutions.</p><p>Choice A is incorrect because the graphs intersect. Choice B is incorrect because the graphs intersect more than once. Choice D is incorrect. It’s not possible for the graph of a quadratic equation and the graph of a linear equation to intersect more than twice.</p><p></p>\n","correct_answer":["C"],"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 \">0</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">1</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">2</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">3</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}}