On a solving of algebraic equations systems associated with context-free languages

Systems of algebraic equations (polynomial and linear) which appear in context-free languages theory are considered. The solution of the system is a set of formal power series expressing one group of variables trough the other group of variables considered as parameters. It is impossible to directly use the classical elimination processes for a non-commutative ring. The conditions of solubility of a polynomial equations system as well as possibility to make lower the order of a linear equations system are given in the article.