Question y-6-x-
One of the two equations in a system of linear equations is given. The system has infinitely many solutions. Which equation could be the second equation in this system?
y = 6 x + 3 One of the two equations in a system of linear
Hard-difficulty · SAT Math · Systems of Two Linear Equations — No-solution and infinite-solution cases. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice D is correct. It’s given that the system has infinitely many solutions. A system of two linear equations has infinitely many solutions when the two linear equations are equivalent. When one equation is a multiple of another equation, the two equations are equivalent. Multiplying each side of the given equation by yields . Thus, is equivalent to the given equation and could be the second equation in the system.
Choice A is incorrect. The system consisting of this equation and the given equation has one solution rather than infinitely many solutions.
Choice B is incorrect. The system consisting of this equation and the given equation has one solution rather than infinitely many solutions.
Choice C is incorrect. The system consisting of this equation and the given equation has no solutions rather than infinitely many solutions.
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