  The aim of this paper is two-fold: (1) introduce four systems of equations
called M-systems and dual M-systems of types $A_{n}$ and $B_{n}$ respectively;
(2) make a connection between M-systems (dual M-systems) and cluster algebras
and prove that the Hernandez-Leclerc conjecture is true for minimal
affinizations of types $A_n$ and $B_n$.
