Think about we have 2 objective functions and both of them are in the form of being equal to zero. For example,
f1: x1^2+x1*x2+2*x2^3=0
f2: 3*x1*x2^2+4*x1+3*x1*x2=0

These functions are just for explaining the case, not real.
And there is also no constraint.

How should I start to solve such a problem?
firstly, should I equal these two functions for getting one objective function, and then should I use any algorithm, like Newton-Raphson, for solving this unconstrained optimization problem? Does it work?

What is the starting point?
Could you help me?
Thanks in advance.