Solving the second equation for y..
2x-y=7 divide both sides by -1
y-2x=-7 add 2x to both sides
y=2x-7
When a solution exists, y=y, so we can say:
2x-7=2x+3 subtract 2x from both sides
-7=3
-1 != 3
Since the above is never true, there are no solutions to this system of equations.
Intuitively, this is because both lines have the same slope, they are parallel, and have an different y-intercept, thus they will never cross each other...