The classical Monte Carlo method is used for the study of properties of the ground state and phase transitions of the spin-pseudospin model describing a two-dimensional Ising magnet with competing charge and spin interactions. This competition causes ground state degeneracy and frustration. 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 histogram analysis of Monte-Carlo data, the type of phase transitions is analyzed. It is found that first order phase transitions are observed near the frustration point, depending on the relationship between the spin s = 1/2 and pseudospin S = 1 interactions.