We 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.