I just don't get this problem, I feel I'm missing something obvious.

Find $\displaystyle dg/du$ if

$\displaystyle 1) x+y= uv$

$\displaystyle

2) xy=u-v

$

and

$\displaystyle

x=g(u,v)$

$\displaystyle y=h(u,v)

$

Poor attempt of solution:

I try to obtain an expression for x as a function of u and v, but I can't seem to be able to get anything from that system of equations.

From 1) I get $\displaystyle x= uv-y$ , but from 2) $\displaystyle y=(u-v)/x$

If I replace into 1) $\displaystyle x=uv-uv/x$

I don't think I'm getting something from that

If $\displaystyle x=g(u,v)$ then

$\displaystyle

g(u,v)=uv-y

$

$\displaystyle

g(u,v)=uv-h(u,v)$

Another thought from there: $\displaystyle dg/du=v-dh/du$

$\displaystyle h(u,v)=y=(u-v)/x $

$\displaystyle dh/du=x$

then,

$\displaystyle dg/du=v-x$ , but $\displaystyle x=g(u,v)$

and I think I'm running in circles here.