  We carry out enhanced symmetry analysis of a two-dimensional Burgers system.
The complete point symmetry group of this system is found using an enhanced
version of the algebraic method. Lie reductions of the Burgers system are
comprehensively studied in the optimal way and new Lie invariant solutions are
constructed. We prove that this system admits no local conservation laws and
then study hidden conservation laws, including potential ones. Various kinds of
hidden symmetries (continuous, discrete and potential ones) are considered for
this system as well. We exhaustively describe the solution subsets of the
Burgers system that are its common solutions with its inviscid counterpart and
with the two-dimensional Navier-Stokes equations. Using the method of
differential constraints, which is particularly efficient for the Burgers
system, we construct a number of wide families of solutions of this system that
are expressed in terms of solutions of the (1+1)-dimensional linear heat
equation although they are not related to the well-known linearizable solution
subset of the Burgers system.
