see if you can see what went wrong:

Assume x=y, it follows that x-y=0. Therefore 2x - 2y=0, so x-y=2x - 2y.

2x - 2y=2(x - y) & x - y=1(x-y)

so 2(x - y)=1(x - y)

divide both by (x - y) to give... 2=1!

isn't maths great?