Question

Which of the following systems has an infinite number of solutions?

A. x+y=1 and x−y=1
B. x+y=1 and x+y=−1
C. x+y=1 and −x−y=−1
D. x+y=1 and x+y=2

Answer 1

C. x+y = 1 and -x-y = -1

Explanation:

Remember that if a system of equations has an infinite number of solutions, then the resulting equation from using the first step of the elimination method would have no variables and would be true.

1) Let's try canceling out the equations in option C, x+y =-1 and -x-y =-1. Add the two equations together. (Work shown in attached picture.)

2) All of the terms cancel out with each other, leaving only a true statement of 0 = 0. Thus, option C is the answer.