Two-dimensional systems of two autonomous polynomial differential equations with homogeneities of the zero, first and second orders are considered with respect to the group of center-affine transformations GL(2,R). The problem of the classification of GL(2,R)-orbits’ dimensions is solved completely for system s(0, 2) with the help of Lie algebra of operators corresponding to GL(2,R) group, and al- gebras of invariants and comitants. A factorsystem s(0, 1, 2)/GL(2, R) for system s(0, 1, 2) is built and with its help two invariant GL(2,R)-integrals are obtained for the system s(1, 2) in some necessary conditions for the existence of singular point of the type ”center”.