{"id":"cb_practice_pdf:t9-math-m1-q19","source_id":"cb_practice_pdf","source_item_id":"t9-math-m1-q19","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":"Part of this question was typeset outside the text flow — a fraction, subscript or similar — and PDF extraction re-inserted it in the wrong place. The wording is reliable; the symbols may be out of order.","form_id":"cb_practice_pdf:test-9","module_number":1,"position":19,"stem":"4x−9y = 9y +5 = 2+4x hy In the given system of equations, h is a constant. If the system has no solution, what is the value of h? −9","stimulus":"","stimulus_html":null,"stem_html":"<p>4x−9y = 9y +5 = 2+4x hy In the given system of equations, h is a constant. If the system has no solution, what is the value of h? −9</p>","rationale_html":"<p>Choice D is correct. A system of two linear equations in two variables, x and y, has no solution if the lines represented by the equations in the xy-plane are distinct and parallel. The graphs of two lines in the xy-plane represented by + = equations in the form Ax By C, where A, B, and C are constants, are parallel if the coefficients for x and y in one equation are proportional to the corresponding coefficients in the other equation. The first equation in the given + = system can be written in the form Ax By C by subtracting 9y from both sides 4 -18 =5 of the equation to yield x y . The second equation in the given system + = can be written in the form Ax By C by subtracting 4x from both sides of the -4 + =2 - equation to yield x hy . The coefficient of x in this second equation, 4, - is 1 times the coefficient of x in the first equation, 4. For the lines to be parallel, - the coefficient of y in the second equation, h, must also be 1 times the -18 =-1 -18 =18 coefficient of y in the first equation, . Thus, h ^ h, or h . 18 Therefore, if the given system has no solution, the value of h is . - Choice A is incorrect. If the value of h is 9, then the given system would have one solution, rather than no solution. Choice B is incorrect. If the value of h is 0, then the given system would have one solution, rather than no solution. Choice C is incorrect. If the value of h is 9, then the given system would have one solution, rather than no solution.</p>","correct_answer":["D"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>0</p>","ord":0},{"label":"B","content_html":"<p>9</p>","ord":1},{"label":"C","content_html":"<p>18</p>","ord":2},{"label":"D","content_html":"","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}