Question

How many solutions does the following system of equations have?

y=x-2
y=-x+2
one solution
no solutions
two solutions
infinitely many solutions

Answer 1

I think it would be two solutions 

Answer 2

x-2=-x+2
x=-x
0=0
Both equations cancel each other out, so any value could be substituted for x in the system of equations and the equation would still be true. Therefore, there are infinitely many solutions.