  The aim of this paper is to apply techniques of symmetry group analysis in
solving two systems of conservation laws: a model of two strictly hyperbolic
conservation laws and a zero pressure gas dynamics model, which both have no
global solution, but whose solution consists of singular shock waves. We show
that these shock waves are solutions in the sense of 1-strong association.
Also, we compute all projectable symmetry groups and show that they are
1-strongly associated, hence transform existing solutions in the sense of
1-strong association into other solutions.
