If you are trying to solve those equations using the equal values method, you would first turn both the equations to equal y. So for x-y=3, you would add y to each side to get x=3+y and then subtract 3 from each side to get x-3=y. When you do the same thing to the equation x=y=7, you get x-7=y. When you plug them together you take away the y's and put an equal sign in between:
x-3=x-7 -then you would subtract x from any side and do that to the other side. You get -3=-7 which isn't correct so you would get a "no solution" problem.