This paper investigates affine control systems with jumps for which the ideal I-f(g(1), ..., g(m)) generated by the drift vector field f in the Lie algebra L(f, g(1), ..., g(m)) can be imbedded as a kernel of a linear first-order partial differential equation. It will lead us to uncontrollable affine control systems with jumps for which the corresponding reachable sets are included in explicitly described differentiable manifolds.