{"id":"cb_question_bank:d270394f-6823-4293-a0d0-d8b198e1f0e9","source_id":"cb_question_bank","source_item_id":"d270394f-6823-4293-a0d0-d8b198e1f0e9","external_id":null,"ibn":"016627-DC","question_id":"2704399f","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":"Which of the following systems of equations has the same solution as the system of equations graphed above?","stimulus":"The figure presents the graph of two intersecting lines in the x y plane with the origin labeled O. The integers negative 5 through 5 are indicated on each axis. One line begins above the x axis and to the left of the y axis, and trends downward and to the right. It crosses the y axis between 0 and 1, then crosses the x axis between 1 and 2, and ends below the x axis and to the right of the y axis. The other line begins below the x axis and slightly to the left of the y axis, and trends upward and to the right. It crosses the y axis at negative 5, then crosses the x axis between 1 and 2, and ends above the x axis and to the right of the y axis. The two lines intersect at the point where both lines cross the x axis between 1 and 2.","stimulus_html":"<div class=\"stimulus_reference \">\n        <div class=\"passage \">\n          <div class=\"prose style:1 \">\n            <div class=\"standalone_image \">\n              <img src=\"/api/assets/01ed2737e5c6d6405ed9a091dd9183f7cd732ed38aa586c1c7a49a065d77a59f\" alt=\"The figure presents the graph of two intersecting lines in the x y plane with the origin labeled O. The integers negative 5 through 5 are indicated on each axis. One line begins above the x axis and to the left of the y axis, and trends downward and to the right. It crosses the y axis between 0 and 1, then crosses the x axis between 1 and 2, and ends below the x axis and to the right of the y axis. The other line begins below the x axis and slightly to the left of the y axis, and trends upward and to the right. It crosses the y axis at negative 5, then crosses the x axis between 1 and 2, and ends above the x axis and to the right of the y axis. The two lines intersect at the point where both lines cross the x axis between 1 and 2.\" width=\"185\" height=\"191\"></div>\n          </div>\n        </div>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following systems of equations has the same solution as the system of equations graphed above?</p>\n","rationale_html":"<p>Choice A is correct. The solution to a system of equations is the coordinates of the intersection point of the graphs of the equations in the <span class=\"italic\">xy</span>-plane. Based on the graph, the solution to the given system of equations is best approximated as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fd7f602488a7d2881669e8289f4f4bb7cd9dca9dc9116bc3f995dace9edd5230\" alt=\"the point with coordinates three halves comma 0\"></span>. In the <span class=\"italic\">xy</span>-plane, the graph of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ce672c12451ce6d730167e9763ac3e67a5ed07d54cba747ed2f59adb20d5d205\" alt=\"y equals 0\"></span> is a horizontal line on which every <span class=\"italic\">y</span>-coordinate is 0, and the graph of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2f9280cb724f9bc73a6cefe3bd4f0836da50ef56ce5749d0fae4a7089dcd5cb2\" alt=\"x equals three halves\"></span> is a vertical line on which every <span class=\"italic\">x</span>-coordinate is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/544c1fbf41c46eecd241e072f3fef539763dd2bbcf0350489f405f9d1fa52c78\" alt=\"three halves\"></span>. These graphs intersect at the point <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fd7f602488a7d2881669e8289f4f4bb7cd9dca9dc9116bc3f995dace9edd5230\" alt=\"with coordinates three halves comma 0\"></span>. Therefore, the system of equations in choice A has the same solution as the given system.</p><p>Choices B, C, and D are incorrect. If graphed in the<span class=\"italic\"> xy</span>-plane, these choices would intersect at the points <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/78db949110eb190c55eb1e590abf1554af93ab72436aa2e37d48feebb975d7ec\" alt=\"with coordinates 0 comma three halves\"></span>, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dd517ff65ad53662b01847047d12b83dfb628a81d6983d27b71cf476b5e02ccf\" alt=\"1 comma 0\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2d4884f132068792fe2bacce12324af4c24c5485d4c44b11eac8f8ba6fec7b13\" alt=\"0 comma 1\"></span>, respectively, not <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fd7f602488a7d2881669e8289f4f4bb7cd9dca9dc9116bc3f995dace9edd5230\" alt=\"the point with coordinates three halves comma 0\"></span>.</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.615000+00:00","source_updated_at":"2023-08-02T20:25:59.615000+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/82abbc951429bd8ad6688c1352ea69419c57e4002931ef33549f9ce0ab815efb\" alt=\"Equation 1: y equals 0. Equation 2: x equals three halves\"></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/2831d9ff1ed9985c1acafe40bebcd3b6d43cdf8050e749aeaaef6b626e6e4171\" alt=\"Equation 1:  y equals three halves. Equation 2: x equals 0\"></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/175150222a6b29b9e020f1903d3497b7bde7b11f3b98625644e1c01a78ce9fd4\" alt=\"Equation 1: y equals 0. Equation 2: x equals 1\"></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/deee10fe12aca303a97667c3e970fe948f7aa6b275299c119df1652c38ae8de8\" alt=\"Equation 1: y equals 1. Equation 2: x equals 0\"></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}}