=>x-2=y^2+xy
=>x-xy-y^2-2=0
=>x(1-y)-y^2+1-3=0
=>x(1-y)+(1-y)(1+y)-3=0
=>(1-y)(x+1+y)=3
=>(x+y+1)(y-1)=-3
=>\(\left(x+y+1;y-1\right)\in\left\{\left(1;-3\right);\left(-3;1\right);\left(-1;3\right);\left(3;-1\right)\right\}\)
=>\(\left(x,y\right)\in\left\{\left(2;-2\right);\left(-6;2\right);\left(-6;4\right);\left(2;0\right)\right\}\)