Explanation
Correct answer: C.
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.
Desmos solution:
Note: The green line overlaps the blue line, confirming the system has infinitely many solutions.
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect. The system consisting of this equation and the given equation has one solution, not infinitely many solutions.
Choice B
Choice B is incorrect. The system consisting of this equation and the given equation has one solution, not infinitely many solutions.
Choice D
Choice D is incorrect. The system consisting of this equation and the given equation has no solution, not infinitely many solutions.