- 15 x + 25 y = 65 One of the two equations in a system of linear equations is

Question

- 15 x + 25 y = 65 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?

Accepted Answer

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 5 yields - 3 x + 5 y = 13 . Dividing both sides of choice C by 4 also yields - 3 x + 5 y = 13 , 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.

Question 87828f