Basic solution (linear programming)

In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions.
For a polyhedron and a vector, is a basic solution if:

All the equality constraints defining are active at
Of all the constraints that are active at that vector, at least of them must be linearly independent. Note that this also means that at least constraints must be active at that vector.

A constraint is active for a particular solution if it is satisfied at equality for that solution.
A basic solution that satisfies all the constraints defining is called a basic feasible solution.