Bivalent or polyvalent cooperative binding between ligand and receptor is much tighter and more efficient than monovalent binding of the same counterparts. Because of this, many biological processes involve polyvalent binding for realization of regulatory mechanisms. For this reason it is necessary to develop a general formalism for prediction of the relationship between the binding affinities of each ligand subunits, the length of the flexible linker between them and avidity of the interaction. Here, we consider an approach that is based on the description of the state of equilibrium for the reaction of mono- and multivalent ligand-receptor binding of algebraic equation systems. This approach allows the evaluation of the avidity of bivalent binding and to determine the concentrations of ligand-receptor complexes, which will be obtained at the equilibrium state. The analysis presented here may be useful in analysing the binding behaviour of a bivalent receptor and a ligand consisting of two subunits covalently connected with a rigid or flexible linker.