Existence of solution for nonlinear (algebraic) equations.

Question

Let

$f_1(x_1,\cdots,x_n)=0$,

$\vdots$

$f_n(x_1,\cdots,x_n)=0,$

be a nonlinear equation. Is there a condition on $f_1,\cdots,f_n$ under which this equation has a solution?

Thanks for your help.