## Implicit function theorem

$\begin{cases}
x+y+uv=0 \\
uxy+v=0
\end{cases}$

Are there any solutions to this system for for $u, v$ in terms of $x, y$ near the point $(x,y,u,v)=(0)$

We cannot apply the implicit function theorem here as the matrix of the partials is not invertible. Is it possible to do a change of coordinates so the jacobian matrix is invertible near (0,0,0,0)?