Easy diophantine equation

If one solves the above Diophantine equation for y in terms of x, this yields:

$y = 9 + \frac{81}{x-9}$ (i)

The numerator in (i) is $81 = 3^4$ , which has 10 integer divisors: $\pm1, \pm3, \pm9, \pm27, \pm81$ . These in turn yield the integer pairs:

$(x,y) = (10,90); (90,10); (12,36); (36,12); (18,18); (8,-72); (-72,8); (6,-18); (-18,6)$

or $\boxed{9}$ total pairs for $x,y \in \mathbb{Z}$ and $x, y \neq 0.$