The Chain Rule & Implicit Differentiation · Challenge problem

The equations $xu + yv^2 = 5$ and $x^2v + yu^3 = 3$ are satisfied at $(x, y, u, v) = (1, 1, 1, 2)$, and near that point they define $u$ and $v$ as differentiable functions of $x$ and $y$. Find $\dfrac{\partial u}{\partial x}$ at $(x, y) = (1, 1)$.