{"id":"cb_question_bank:443cb8b9-593c-4aab-99eb-1823714c398f","source_id":"cb_question_bank","source_item_id":"443cb8b9-593c-4aab-99eb-1823714c398f","external_id":null,"ibn":"022962-DC","question_id":"6e6a3241","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":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following graphs in the xy -plane could be used to solve the system of equations above?","stimulus":"Equation 1: x plus 5 y, equals 5. Equation 2: 2 x minus y, equals negative 4","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7bdea498d894101894437f0cf19dfdbdc5facb3a19fb4d23be3cb0bf0ab69ad6\" alt=\"Equation 1: x plus 5 y, equals 5. Equation 2: 2 x minus y, equals negative 4\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following graphs in the <span class=\"italic \">xy</span>-plane could be used to solve the system of equations above?</p>\n","rationale_html":"<p>Choice C is correct. The graph of a system of equations is the graph that shows the lines represented by each of the equations in the system. The <span class=\"italic\">x</span>-intercept of the graph of each given equation can be found by substituting 0 for <span class=\"italic\">y</span> in each equation: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7a396161f1559ed34f2a9c5b5848b307cdede959626e9656f49ab74457582932\" alt=\"x plus, 5 times 0, equals 5\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/24796268b6fb782d78745c6cfef1c4479da9853b4b07eafd4bc226fb068e3bc1\" alt=\"x equals 5\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e7efe939f635e9f4a3d775463ce82fe3664a7ed65e5a6bae5fd6c71a553ed7b8\" alt=\"2 x minus 0, equals negative 4\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0edd49746d3055df6f32b5efedf4de1882d140a0d4f3698f8fb73b2b3693633b\" alt=\"x equals negative 2\"></span>. The <span class=\"italic\">y</span>-intercept of the graph of each equation can be found by substituting 0 for <span class=\"italic\">x</span> in each equation: <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ee46aeafd70d9d2ea29418103c223207402a7b7430e27c029774c23a970ab6e6\" alt=\"0 plus 5 y, equals 5\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cc0d4aec836ba9b82085d477b7ea166b87d9abd1486c2dd63be7e952b395ed15\" alt=\"y equals 1\"></span>, and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4f2189475c78ad0da949900e59bdd6b6379890a7b43d27416cc0aa37bb1f0903\" alt=\"2 times 0, minus y, equals negative 4\"></span> or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/365d9f5d9b81010454782b3469da46ef190dc0cfe2a2d209adba7c5a64556429\" alt=\"y equals 4\"></span>. Using these <span class=\"italic\">x</span>- and <span class=\"italic\">y</span>- intercept values, the line that has equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2532c9dd678b8ac89731e2e94f362d7a5b712464b66a02f85df1ba527d38ed67\" alt=\"x plus 5 y, equals 5\"></span> passes through the points <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6f3a9226f302010cb970c4c9a7ec50c741c7d5a2c55111fb791bcf92be5e5159\" alt=\"with coordinates 0 comma 1\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/446bde04eb6741873ebf353639a45e57f15896914d6ae14051c10dd24c7aba06\" alt=\"5 comma 0\"></span>, and the line that has equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f7e4b38d1d519c8dcaae61e199be55e80ed42be6059527789ea7a3231dd1ad7f\" alt=\"2 x minus y, equals negative 4\"></span> passes through the points <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d733af07db4a0ffb955944e977bb44a1ef279a092b1517e7acf09caf1a336c4f\" alt=\"with coordinates 0 comma 4\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/807b360cf22ee982e870a531b136bc7523c8d019a8e56cad4e9bcf281058ba91\" alt=\"negative 2 comma 0\"></span>. Only the lines in choice C pass through these points and can be used to solve the given system of equations.</p><p>Choices A, B, and D are incorrect. In choices A and B, neither line passes through <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6f3a9226f302010cb970c4c9a7ec50c741c7d5a2c55111fb791bcf92be5e5159\" alt=\"the points with coordinates 0 comma 1\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/446bde04eb6741873ebf353639a45e57f15896914d6ae14051c10dd24c7aba06\" alt=\"5 comma 0 \"></span> or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d733af07db4a0ffb955944e977bb44a1ef279a092b1517e7acf09caf1a336c4f\" alt=\"the points with coordinates 0 comma 4\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/807b360cf22ee982e870a531b136bc7523c8d019a8e56cad4e9bcf281058ba91\" alt=\"negative 2 comma 0\"></span>. In choice D, although one line passes through <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d733af07db4a0ffb955944e977bb44a1ef279a092b1517e7acf09caf1a336c4f\" alt=\"the points with coordinates 0 comma 4\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/807b360cf22ee982e870a531b136bc7523c8d019a8e56cad4e9bcf281058ba91\" alt=\"negative 2 comma 0 \"></span> the other line doesn’t pass through <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6f3a9226f302010cb970c4c9a7ec50c741c7d5a2c55111fb791bcf92be5e5159\" alt=\"the points with coordinates 0 comma 1 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/446bde04eb6741873ebf353639a45e57f15896914d6ae14051c10dd24c7aba06\" alt=\"5 comma 0\"></span>.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.618000+00:00","source_updated_at":"2023-08-02T20:25:59.618000+00:00","options":[{"label":"A","content_html":"<p><img src=\"/api/assets/02896e1ae15d936ac9c43fbd7c33dba4784725d7d18610286551d5ae7535bfc5\" alt=\"The answer choice presents the graph of two lines in the x y plane. The numbers negative 4 and 4 are indicated on each axis. One line slants upward and to the right. It crosses the x axis at negative 5, and crosses the y axis at 1. The other line slants downward and to the right. It crosses the y axis at 4, and crosses the x axis at 2. The two lines intersect above the x axis and to the right of the y axis.\" width=\"86\" height=\"92\"></p>\n","ord":0},{"label":"B","content_html":"<p><img src=\"/api/assets/319381e9536d8498b198d01a96b95128c5bf446eea4aafca41dce2c660b6f814\" alt=\"The answer choice presents the graph of two lines in the x y plane. The numbers negative 4 and 4 are indicated on each axis. One line slants upward and to the right. It crosses the y axis at negative 4, and crosses the x axis at 4. The other line slants downward and to the right. It crosses the y axis at 1, and crosses the x axis at 1. The two lines intersect below the x axis and to the right of the y axis.\" width=\"86\" height=\"91\"></p>\n","ord":1},{"label":"C","content_html":"<p><img src=\"/api/assets/6d63d742fb9539ab30a791f56ae1799dc10b59d3f9f5347f03795500a70b2b04\" alt=\"The answer choice presents the graph of two lines in the x y plane. The numbers negative 4 and 4 are indicated on each axis. One line slants upward and to the right. It crosses the x axis at negative 2, and crosses the y axis at 4. The other line slants downward and to the right. It crosses the y axis at 1, and crosses the x axis at 5. The two lines intersect above the x axis and to the left of the y axis.\" width=\"87\" height=\"91\"></p>\n","ord":2},{"label":"D","content_html":"<p><img src=\"/api/assets/ac4beb456c8cfaaaecab26db0b84433227a8d16c40d9fcab830542aeb52651d7\" alt=\"The answer choice presents the graph of two lines in the x y plane. The numbers negative 4 and 4 are indicated on each axis. One line slants upward and to the right. It crosses the x axis at negative 2, and crosses the y axis at 4. The other line slants upward and to the right. It crosses the y axis at negative 1, and crosses the x axis at 5. The two lines intersect below the x axis and to the left of the y axis.\" width=\"87\" height=\"93\"></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}}