  This paper explores the nature of the solution sets of systems of equations
in virtually abelian groups. We view this question from two angles. From a
formal language perspective, we prove that the set of solutions to a system of
equations forms an EDT0L language, with respect to a natural normal form.
Looking at growth, we show that the growth series of the language of solutions
is rational. Furthermore, considering the set of solutions as a set of tuples
of group elements, we show that it has rational relative growth series with
respect to any finite generating set.
