The equation 4x-y=3 can be written y=4x-3.
If this is graphed it will be a line passing through (0,-3) and (3/4,0).
Draw a square at points (0,0), (0,5), (5,5) and (5,0) and the part of the line enclosed by the square contains the only solutions available within the set of integers.
The only two are x=y=1 and x=2, y=5.