Consider system of nonlinear equations:
$2a-2b-3=0$
$a-a^2-b-2ab-b^2=0$
If you replace variables this way: $x=a+b$, $y=a-b$, then this system can be simplified to $2y=3,y=x^2$. My question is following: having big multivariate system of linear and squared terms, is it possible to find linear replacement for unknowns, such that number of terms is less then in initial system?