I have a quick question for a problem I am solving:
I am solving a non-linear system of $4$ equations with $4$ variables, and after brute expansion I have deduced that there are $24$ solutions (but only one set of unique values which can be changed to make different solutions). But I am wondering if there is a faster way for non-linear simultaneous equations to determine the number of solutions there are - is there a set for only a certain number of solutions, no solutions, infinite solutions, etc.
Any help is appreciated.
There is no specified way to solve non-linear equations due to the vast, unrestrictive nature of them. Thus, another way must be employed in order to solve each different set of equations.