We consider Weil-Roshevskiy axiomatic system os adopted variant of the point-vector axiomatic system for affine space, which is the basement of the analytic geometry and algebra of finite-dimensional spaces. It gives us an opportunity to obtain strictly proved statements in vector algebra. We give here four groups of axioms and а set of traditionally proved theorems, some of them with proof. A construction of affine manifold (n-dimensional plane) possesses а geometric meaning of the generalization of the line and the plane. In this connection we consider on exercise of reducing a parametric vector equation of n-dimensional plane to matrix equation. Also we discuss the notions of geometrically dependent vector set, convex span, and simplex.