  A class of two-dimensional systems of second-order ordinary differential
equations is identified in which a system requires fewer Lie point symmetries
than required to solve it. The procedure distinguishes among those which are
linearizable, complex-linearizable and solvable systems. We also present the
underlying concept diagrammatically that provides an analogue in $\Re^{3}$ of
the geometric linearizability criteria in $\Re^2$.
