Quite easy for olympiad..

Can anyone tell me how to complete this sum using the following approach? Given, $2x+7y \mid 7x+2y$ $\implies 2x+7y \mid (2x+7y) + 5(x-y)$ $\implies 2x+7y \mid 5(x-y)$ Now, how do I complete the sum from here?

Trying to get the values for which division can holds. Indeed $x=y$ evidently works. Since $x\ge y$ we have $3>\frac{5(x-y)}{2x+7y}\ge 1$. So we get the above solutions taking $2(2x+7y)=5(x-y)$ and $2x+7y=5(x-y)$.