A method for accounting for the influence of the outer surface on the internal state of the electron ― ion system for nanoparticles is proposed. The estimated interaction energy of the representative elements of the components (LaB6, MeB2) is part of the composite depending on the size of the nanoplate. The characteristic parameters of the eutectic of quasi-binary boride-boride systems are calculated and analytically presented. During the transition of bulk materials to nanomaterials, the melting temperature of the eutectic decreases, and the concentration ratio of the components changes. With the help of first-principle methods the scheme of calculation of energy of interaction of representative elements of components from the first principles is developed. The dependence of the interaction energy of the representative elements on the sizes of the materials is analytically obtained. It is proved that the reduction of the size of the eutectic composite leads to a significant decrease in the melting temperature at the eutectic point, as well as to a change in the concentration ratio of the components. The obtained analytical formulas allow to estimate the change of concentration and melting temperature at the eutectic point depending on the thickness of the nanocomposite. Keywords: electron-ion system energy, pseudopotential method, nanosystem, nanoplate surface energy, concentration and melting point at the eutectic point.