Let $X = \{x_1,...,x_n\}$ be a set of variables and $F = \{f_1(\tilde{X}_1)=0,...,f_m(\tilde{X}_m)=0\}$ be a set of $m \ge n$ equations, each one a function of some subset $\tilde{X}_i \subset X$. I know that my set of equations is sufficient for solving for all variables $x_i$, although some may be redundant. Furthermore, I know that this solution can be found in closed form.
Is there any special term for such a system? I suppose it's more specific than just "system of equations", since a general system might not have a closed-form solution, or any solutions at all.