We investigate the phase diagram of a two-dimensional driven-dissipative system of polaritons coupled to an excitonic reservoir. We find that two critical points exists. The first corresponds to the quasicondensation and the second to a first-order phase transition from the nonuniform state with spatially modulated density to a uniform state. The latter is related to the modulational instability of a homogeneous state due to the repulsive interactions with the noncondensed reservoir. The first-order character of the transition is evidenced by a discontinuity in the density and the correlation length as well as the phase coexistence and metastability. Moreover, we show that a signature of a Berezinskii-Kosterlitz-Thouless-like transition can be observed in the nonuniform phase
