  The purpose of this present paper is to investigate the geometric structure
of regular overdetermined systems of second order with two independent and one
dependent variables from the point of view of rank 2 prolongations. Utilizing
this notion of prolongations, we characterize the type of these overdetermined
systems. We also give a systematic method for constructing the geometric
singular solutions by analyzing of a decomposition of this prolongation. As an
applications, we determine the geometric singular solutions of Cartan's
overdetermined systems.
