Question

if you have the system y=3x-1 and y=2x+8 why can you create the equation 3x-1=2x+8?

Answer 1

Because you have allowed y to equal both of them, you can set them equal to each other.

Answer 2

See, there is a point where the two lines intersect. That is where the two equations are equal to each other: http://www.wolframalpha.com/input/?i=y%3D3x-1+and+y%3D2x%2B8