I am new in working with system of equations. I know that: for linear systems of equations, one can check if the equations are linearly independent to prove if the system has a solution or not.
What methods can be used to prove that a system of non linear equations (indeed algebraic equations) has a solution ?
Does the number of equations hsould be also $n$ ( as the number of unknowns is $n$) ?
Any reference in this manner would be great.
thank you in advance.