When y=- 1, x+y is the smallest, which is-1/2.

You can understand by drawing a picture that the minimum value must be the boundary (because if it is not the boundary, x+y will be smaller if it moves horizontally to the left or vertically downwards).

Then on the boundary, x+y = (1/2) * (y+1) 2-1/2.

Therefore, when y=- 1, x+y is the smallest, which is-1/2.