  The classical Monte Carlo method is used to study the properties of the
ground state and phase transitions of the spin-pseudospin model, which
describes a two-dimensional Ising magnet with competing charge and spin
interactions. This competition leads to the ground state degeneracy and the
frustration of the system. It is shown that the ground state degeneracy is
observed in the frustration area with nonzero probabilities of the formation of
two different ordered states. Based on the histogram analysis of the Monte
Carlo data, the type of phase transitions is analyzed. It is found that, near
the frustration point, first-order phase transitions are observed in the
dependence on the ratio between the spin ($s = 1/2$) and pseudospin ($S = 1$)
interactions.
