How to solve these linear and quadratic equations? Ok, this may seem simple to some, but I spent so long trying to solve these equations and I wasn't able to:
$x+xy+y=19$
$x^2y+y^2x=84$
I'm finding the pairs of possible x-y values. (x and y are interchangeable, so if (1, 2) is a solution then so is (2, 1))
Can anyone help with this? Every time I tried this I ended up with some stupidly complicated quadratic relation.

Put $$z=xy$$
then you have
$$x+y+z=19$$
$$z(x+y)=84=z(19-z)$$
so
$$z^2-19z+84=0$$
You can finish.
