  We prove finite time supercritical blowup in a parity-time-symmetric system
of the two coupled nonlinear Schr\"odinger (NLS) equations. One of the
equations contains gain and the other one contains dissipation such that
strengths of the gain and dissipation are equal. We address two cases: in the
first model all nonlinear coefficients (i.e. the ones describing self-action
and non-linear coupling) correspond to attractive (focusing) nonlinearities,
and in the second case the NLS equation with gain has attractive nonlinearity
while the NLS equation with dissipation has repulsive (defocusing) nonlinearity
and the nonlinear coupling is repulsive, as well. The proofs are based on the
virial technique arguments. Several particular cases are also illustrated
numerically.
