Question 15-x-2
One of the two equations in a system of linear equations is given. The system has infinitely many solutions. Which of the following could be the second equation in the system?
- 15 x + 25 y = 65 One of the two equations in a system
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 C 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. Dividing both sides of the given equation by yields . Dividing both sides of choice C by also yields , so choice C is equivalent to the given equation. Thus, choice C 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, not infinitely many solutions.
Choice B is incorrect. The system consisting of this equation and the given equation has one solution, not infinitely many solutions.
Choice D is incorrect. The system consisting of this equation and the given equation has no solution, not infinitely many solutions.
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