xy-10(x+y)=1
xy-10x-10y+100=101
(x-10)(y-10)=101
①
x-10=1
y-10=101
x=11,y=111
②
x-10=-1
y-10=-101
x=9,y=-91
整数解为:
x=11,y=111
x=111,y=11
x=-9,y=-91
x=-91,y=-9