Given that \(x\) and \(y\) are functions of \(u\) and \(v\) defined by \(f(x,y,u,v)=0\) and \(\phi(x,y,u,v)=0\), find \(\frac{\partial x}{\partial u}\) in terms of partial derivatives of \(f\) and \(\phi\) with respect to \(x, y, u\) and \(v\). If \begin{align*} x^2+y^2-25uv &= 0, \\ ux+vy-1 &= 0, \end{align*} prove that \(\frac{\partial x}{\partial u} = \pm \frac{1}{14}\) when \(u=v=1\), and give the reason for the ambiguity in sign.