Solve each of the following systems, if possible. Indicate whether the system has a unique solution, infinitely many solutions, or no solution. I can either use substitution or elimination in this problem.

Question

y=2-x
y=x-2
I did it already by using the substitution method and got an answer as (2,0). I just need to know if the system has a unique solution (I chose the unique solution option but I'm not sure if I'm right), infinitely many solutions, or no solution? I want to check with you guys if I'm doing this right! I started the problem like this x-2=2-x by substituting y=x-2. Please answer and don't ignore! :(

Answer 1

Since 2-x = -(x-2), you have y = -y
So, y=0
so 2-x = 0, and x=2
That is the only solution. You have two lines with different slopes, so the must intersect in exactly one point.