Reformulation of algebraic differential equation into ODE [on hold]

Consider algebraic differential equations
{x′(t)=f(t,x,z)(∗)0=g(t,x)\begin{cases}
& x'(t)=f(t,x,z) \qquad (*)\\
& 0= g(t,x)
\end{cases}
if ∂g∂x⋅∂f∂z\frac{\partial g}{\partial x} \cdot \frac{\partial f}{\partial z} is non-singular, then we can reformulate (*) as ordinary differential equations.

I have no idea to solve the question. Can anyone help me!

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