  In this paper, we re-investigate the resolution of Toeplitz systems $T u =g$,
from a new point of view, by correlating the solution of such problems with
syzygies of polynomials or moving lines. We show an explicit connection between
the generators of a Toeplitz matrix and the generators of the corresponding
module of syzygies. We show that this module is generated by two elements of
degree $n$ and the solution of $T u=g$ can be reinterpreted as the remainder of
an explicit vector depending on $g$, by these two generators.
