2x-y=3 meets y=1 when 2x-1=3, 2x=4, x=2, that is, at (2,1).
2x-y=3 meets y=-3 when 2x+3=3, x=0, that is, at (0,-3).
These two points are the rightmost limits of the region bounded by -3≤y≤1, that is, for y in [-3,1]. The maximum positive point is (2,1) corresponding to max(x,y).
If x can be negative, then the minimum cannot be defined because it’s at (-∞,-3). But if x is positive the minimum is (0,-3).