y = 6x+18 One of the equations in a system of two linear equations is given. The system has no solution. Which equation could be the second equation in the system? −6x+y = 18
","rationale_html":"Choice B 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 + = parallel and distinct. Lines represented by equations in standard form, Ax By C + = and Dx Ey F, are parallel if the coefficients for x and y in one equation are proportional to the corresponding coefficients in the other equation, meaning 46 SAT PRACTICE TEST #8 ANSWER EXPLANATIONS SAT ANSWER EXPLANATIONS n MATH: MODULE 2 D=E F ; and the lines are distinct if the constants are not proportional, meaning is A B C D E =6 +18 not equal to or . The given equation, y x , can be written in standard A B -6 + =18 form by subtracting 6x from both sides of the equation to yield x y . + = =- Therefore, the given equation can be written in the form Ax By C, where A 6, = =18 -6 + =22 B 1, and C . The equation in choice B, x y , is written in the form + = =- = = D=- 6 Dx Ey F, where D 6, E 1, and F 22. Therefore, - , which can be A 6 22 rewritten as D= 1; E=1 , which can be rewritten as E= 1; and F= 18, which can be A 11B 1 B C rewritten as F= 9. Since D= 1, E= 1, and F is not equal to 1, it follows that the C A B C -6 + =22 given equation and the equation x y are parallel and distinct. Therefore, a system of two linear equations consisting of the given equation and the equation -6 + =22 x y has no solution. Thus, the equation in choice B could be the second equation in the system. -6 + =18 Choice A is incorrect. The equation x y and the given equation represent the same line in the xy-plane. Therefore, a system of these linear equations would have infinitely many solutions, rather than no solution. Choice C is incorrect. The -12 + =36 equation x y and the given equation represent lines in the xy-plane that are distinct and not parallel. Therefore, a system of these linear equations would have exactly one solution, rather than no solution. Choice D is incorrect. The -12 + =18 equation x y and the given equation represent lines in the xy-plane that are distinct and not parallel. Therefore, a system of these linear equations would have exactly one solution, rather than no solution.
","correct_answer":["B"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"−6x+y = 22
","ord":0},{"label":"B","content_html":"−12x+y = 36
","ord":1},{"label":"C","content_html":"−12x+y = 18
","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}}