The existing literature discusses different strategies to solve a scalar
ordinary differential equation using Lie point symmetries. We focus on
three of these strategies in order to frame methods for finding
solutions of non-linear systems of ordinary differential equations.
These include Lie's integration theorem, method of successive reduction
of order and the method of using the invariants of the admitted symmetry
generators. Illustrative examples and those taken from mechanics are
presented to highlight the use of these methods.