According to the authors, the results of the theory of linear inequalities should be more widely used in machine learning problems. To eliminate redundant inequalities when constructing ensembles based on linear separators, one should use theorems on dependent inequalities and consequences. To generalize the results of various studies, search models for the most compatible subsystems should be used. The concept of maximally collaborative subsystems should be expanded to include unanimity committees. To solve classification problems, one can effectively use the method of convex hulls, and to determine the extreme points of convex hulls, use the results from the theory of alternative systems. The article provides the information necessary for this from the theory of linear inequalities, mathematical models based on them and a listing of programs for the computer implementation of mathematical models.