We first investigate the general properties of the system and identify all possible wave combinations. Second, a critical investigation of the Riemann problem yields definite results for large data about the existence of Riemann solutions made of Lax shocks, rarefaction waves, and admissible stationary contacts. In some range of Riemann data, no solution exists. We can identify relatively large neighborhoods of Riemann data in which the Riemann problem admits a unique solution.