We investigate symmetries and reductions of a coupled KdV system with variable coefficients. The infinitesimals of the group
of transformations which leaves the KdV system invariant and
the admissible forms of the coefficients are obtained using the
generalized symmetry method based on the Fréchet derivative of
the differential operators. An optimal system of conjugacy
inequivalent subgroups is then identified with the adjoint action
of the symmetry group. For each basic vector field in the optimal
system, the KdV system is reduced to a system of
ordinary differential equations, which is further studied with the
aim of deriving certain exact solutions.