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This paper concerns about the weak unique continuation property of solutionsof a general system of differential equation/inequality with a second orderstrongly elliptic system as its leading part. We put not only some naturalassumption which called {\sl basic assumptions}, but also some technicalassumptions which we called {\sl further assumptions}. It is shown as usual byfirst applying the Holmgren transform to this inequality and then establishinga Carleman estimate for the leading part of the transformed inequality. TheCarleman estimate given via a partition of unity and Carleman estimate for theoperator with constant coefficients obtained by freezing the coefficients ofthe transformed leading part at a point. A little more details about this areas follows. Factorize this operator with constant coefficients into two firstorder differential operators. Conjugate each factor by a Carleman weight andderive an estimate which is uniform with respect to the point at which we frozethe coefficients for each conjugated factor by constructing a parametrix forits adjoint operator.

Unique continuation property of solutions to general second order elliptic systems