Solution set

In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.
For example, for a set formula_1 of polynomials over a ring formula_2,
the solution set is the subset of formula_2 on which the polynomials all vanish (evaluate to 0), formally
The feasible region of a constrained optimization problem is the solution set of the constraints.
Remarks.
In algebraic geometry, solution sets are called algebraic sets if there are no inequalities. Over the reals, and with inequalities, there are called semialgebraic sets.
Other meanings.
More generally, the solution set to an arbitrary collection "E" of relations ("Ei") ("i" varying in some index set "I") for a collection of unknowns formula_7, supposed to take values in respective spaces formula_8, is the set "S" of all solutions to the relations "E", where a solution formula_9 is a family of values formula_10 such that substituting formula_11 by formula_9 in the collection "E" makes all relations "true".
The above meaning is a special case of this one, if the set of polynomials "fi" if interpreted as the set of equations "fi"("x")=0.