How do i solve a set of equations that are set equal to eachother?

I assume you have two equations, since more than that might not make sense

so, suppose you have

y = x^2+3x-9
y = 2x-7

then, as you said, set them equal to each other, and you have

x^2+3x-9 = 2x-7
x^2+x-2 = 0
Now just solve that as usual.