Omitting Unary and Affine Types

In this manuscript we examine the possibility of describing some properties of finite algebras by systems consisting of constant number of term-equations. More precisely we are interested in describing finite algebras omitting Hobby-McKenzie types 1 and 2 by systems of linear identities on two at most ternary terms. It is shown that there exists a single system on two ternary terms that might describe this property. However, whether it does or not remains for further examination.