  This paper concerns about the weak unique continuation property of solutions
of a general system of differential equation/inequality with a second order
strongly elliptic system as its leading part. We put not only some natural
assumption which called {\sl basic assumptions}, but also some technical
assumptions which we called {\sl further assumptions}. It is shown as usual by
first applying the Holmgren transform to this inequality and then establishing
a Carleman estimate for the leading part of the transformed inequality. The
Carleman estimate given via a partition of unity and Carleman estimate for the
operator with constant coefficients obtained by freezing the coefficients of
the transformed leading part at a point. A little more details about this are
as follows. Factorize this operator with constant coefficients into two first
order differential operators. Conjugate each factor by a Carleman weight and
derive an estimate which is uniform with respect to the point at which we froze
the coefficients for each conjugated factor by constructing a parametrix for
its adjoint operator.
