The steady, supersonic, uniform flow of an inviscid perfect gas passing successively through a simple Prandtl-Mayer expansion r and a shock j which have one direction is studied. The system of two waves S2 = { r,j } is specified by the Mach number M and the net angle of freestream turning βs. Analytical solutions are given which make it possible to determine monotonic and nonmonotonic ranges of gas-dynamic variables behind the system to calculate the wave strengths when the system is optimal.