  A generalisation of the Lie symmetry method is applied to classify a coupled
system of reaction-diffusion equations wherein the nonlinearities involve
arbitrary functions in the limit case in which one equation of the pair is
quasi-steady but the other not. A complete Lie symmetry classification,
including a number of the cases characterised being unlikely to be identified
purely by intuition, is obtained. Notably, in addition to the symmetry analysis
of the PDEs themselves, the approach is extended to allow the derivation of
exact solutions to specific moving-boundary problems motivated by biological
applications tumour growth). Graphical representations of the solutions are
provided and biological interpretation addressed briefly. The results are
generalised on multi-dimensional case under assumption of radially symmetrical
shape of the tumour.
