The four-dimensional affine differential system is considering, whose analog in the five-dimensional case expresses influence of indices of energy safety on the indices of economic safety (the energy complex of the Republic of Moldova is taken as an example). The study of integrals of this system allows predicting the modification of one index while the fluctuation of the others. This can give important information for the correct administering of the energy complex of the Republic. The factor-system and admitted Lie algebra of operators are obtained for the four-dimensional differential system. With the aid of this algebra the first integral for the factor-system is obtained, that is a determinant of the matrix, constructed on coordinate vectors of the Lie algebra operators. Found integral gives the possibility to construct the first invariant integral for the initial system with respect to centroaffine group.