Elimination theory

Part of algebraic geometry devoted to the elimination of variables between polynomials

The field of elimination theory was motivated by the need of methods for solving systems of polynomial equations.

One of the first results was Bézout's theorem, which bounds the number of solutions (in the case of two polynomials in two variables at Bézout time).

Except for Bézout's theorem, the general approach was to eliminate variables for reducing the problem to a single equation in one variable.