Help with two variable equation

Question

I need help with this equation which was given to my son who is in 4rth grade.

Solve in positive integers the equation: $xy=10(x+y)$.

Answer 1

$xy =10x+10y$ $\implies$ $y=\frac {10x}{x-10}$.
Now use hit and trial or you can easily see that y has an integral value when x equals an integral value of 10 except 1.

Answer 2

HINT:

$$(x-m)(y-m)=xy-m(x+y)+m^2$$

Answer 3

To follow up on lab's excellent hint, that means that $(x-10)(y-10)=100$, so you can have $(x,y)=(20,20),(35,14),(60,12),(30,15),(110,11)$ (and also swapping $x,y$). A 4th grader might find one of these by trial and error.