(x-1)×(y+2)=7
<=>xy+2x-y-2=7
<=>(xy+2x)-(y-2)=7
<=>x(y+2)-(y+2)=7
<=>(y+2)(x-1)=7
Theo đề bài ta có:
(y+2)(x-1)=7 nên y+2, x-1 ∈ Ư(7)
Vì 7=1.7=-1.(-7)
Nên ta có: $\left \{ {{y+2=7} \atop {x-1=1}} \right.$ <=>$\left \{ {{y=5} \atop {x=2}} \right.$
$\left \{ {{y+2=1} \atop {x-1=7}} \right.$ <=>$\left \{ {{y=-1} \atop {x=8}} \right.$
$\left \{ {{y+2=-7} \atop {x-1=-1}} \right.$ <=>$\left \{ {{y=-9} \atop {x=0}} \right.$
$\left \{ {{y+2=-1} \atop {x-1=-7}} \right.$ <=>$\left \{ {{y=-3} \atop {x=-6}} \right.$
Vậy x,y ∈ (2;5);(8;-1);(0;-9);(-6;-3).
