xy = x+y or x+y = -xy

the only solution is when x and y = 2 or x and y = -2

suppose y>x

then we can say y=kx+r k is an integer r<x

the left side is a multiple of x so the right should be so should x divides r but x>r then r=0

so y = kx

divde both sides by x

but x is an integer so k should equal 1

and

other case x+y = -xy same

so xy both 2 or both -2