The following is from a list of problems that, as far as I know, all have solutions. Unfortunately, I don't have a list of solutions.

Solve the following system, where $\displaystyle x > y$:

$\displaystyle x + y + xy = 19$

$\displaystyle xy(x + y) = 84$

The answer is $\displaystyle x=4, y=3$. I don't know if there is another solution, and I got it simply by inspection - is there an algebraic method to get the answer (or a reason why it isn't algebraically solvable)?

Thanks!