{"id":"cb_question_bank:0dc81d34-6ad5-4aab-b0f6-0e753be212d5","source_id":"cb_question_bank","source_item_id":"0dc81d34-6ad5-4aab-b0f6-0e753be212d5","external_id":"deb03694-cf78-40ff-a84f-f782eba08ba4","ibn":null,"question_id":"cfe67646","program":"SAT","module":"math","domain_code":"H","domain":"Algebra","skill_code":"H.E.","skill":"Linear inequalities in one or two variables","difficulty":"E","score_band":3,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The point left parenthesis 8 comma 2 right parenthesis in the xy -plane is a solution to which of the following systems of inequalities?","stimulus":"","stimulus_html":null,"stem_html":"<p>The point&nbsp;<math alttext=\"left parenthesis 8 comma 2 right parenthesis\"><mo>(</mo><mrow><mn>8</mn></mrow><mo>,</mo><mrow><mn>2</mn></mrow><mo>)</mo></math> in the <em>xy</em>-plane is a solution to which of the following systems of inequalities?</p>","rationale_html":"<p style=\"text-align: left;\">Choice A is correct. The given point,&nbsp;<math alttext=\"left parenthesis 8 comma 2 right parenthesis\"><mfenced><mrow><mn>8</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math>, is located in the first quadrant in the <em>xy</em>-plane. The system of inequalities in choice A represents all the points in the first quadrant in the <em>xy</em>-plane. Therefore,&nbsp;<math alttext=\"left parenthesis 8 comma 2 right parenthesis\"><mfenced><mrow><mn>8</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math> is a solution to the system of inequalities in choice A.</p>\n<p style=\"text-align: left;\">Alternate approach: Substituting <math alttext=\"8\"><mn>8</mn>\n</math> for <math alttext=\"x\"><mi>x</mi>\n</math> in the first inequality in choice A, <math alttext=\"x greater than 0\"><mi>x</mi><mo>&gt;</mo><mn>0</mn></math>, yields&nbsp;<math alttext=\"8 greater than 0\"><mn>8</mn><mo>&gt;</mo><mn>0</mn></math>, which is true. Substituting <math alttext=\"2\"><mn>2</mn>\n</math> for <math alttext=\"y\"><mi>y</mi>\n</math> in the second inequality in choice A,&nbsp;<math alttext=\"y greater than 0\"><mi>y</mi><mo>&gt;</mo><mn>0</mn></math>, yields&nbsp;<math alttext=\"2 greater than 0\"><mn>2</mn><mo>&gt;</mo><mn>0</mn></math>, which is true. Since the coordinates of the point&nbsp;<math alttext=\"left parenthesis 8 comma 2 right parenthesis\"><mfenced><mrow><mn>8</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math> make the inequalities <math alttext=\"x greater than 0\"><mi>x</mi><mo>&gt;</mo><mn>0</mn></math> and&nbsp;<math alttext=\"y greater than 0\"><mi>y</mi><mo>&gt;</mo><mn>0</mn></math> true, the point&nbsp;<math alttext=\"left parenthesis 8 comma 2 right parenthesis\"><mfenced><mrow><mn>8</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math> is a solution to the system of inequalities consisting of <math alttext=\"x greater than 0\"><mi>x</mi><mo>&gt;</mo><mn>0</mn></math> and&nbsp;<math alttext=\"y greater than 0\"><mi>y</mi><mo>&gt;</mo><mn>0</mn></math>.</p>\n<p style=\"text-align: left;\">Choice B is incorrect. This system of inequalities represents all the points in the fourth quadrant, not the first quadrant, in the <em>xy</em>-plane.</p>\n<p style=\"text-align: left;\">Choice C is incorrect. This system of inequalities represents all the points in the second quadrant, not the first quadrant, in the <em>xy</em>-plane.</p>\n<p style=\"text-align: left;\">Choice D is incorrect. This system of inequalities represents all the points in the third quadrant, not the first quadrant, in the <em>xy</em>-plane.</p>","correct_answer":["A"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.820000+00:00","source_updated_at":"2023-08-02T20:25:59.820000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"x greater than 0\"><mi>x</mi><mo>&gt;</mo><mn>0</mn></math></p>\n<p><math alttext=\"y greater than 0\"><mi>y</mi><mo>&gt;</mo><mn>0</mn></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"x greater than 0\"><mi>x</mi><mo>&gt;</mo><mn>0</mn></math></p>\n<p><math alttext=\"y less than 0\"><mi>y</mi><mo>&lt;</mo><mn>0</mn></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"x less than 0\"><mi>x</mi><mo>&lt;</mo><mn>0</mn></math></p>\n<p><math alttext=\"y greater than 0\"><mi>y</mi><mo>&gt;</mo><mn>0</mn></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"x less than 0\"><mi>x</mi><mo>&lt;</mo><mn>0</mn></math></p>\n<p><math alttext=\"y less than 0\"><mi>y</mi><mo>&lt;</mo><mn>0</mn></math></p>","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}}