On a solvable system of difference equations of sixth-order

In this paper, we study the following two-dimesional system of difference equations (Formula presented.), (Formula presented.), n ? N0; where the parameters a,b,c,d and the initial values x-i,y-i, i ? {1,2,3,4,5,6}, are real numbers. We show that some subclasses of nonlinear two-dimensional system of difference equations are solvable in closed form. We also describe the forbidden set of solutions of the system of difference equations. Some numerical examples are given to demonstrate the theoretical results. © 2023 Miskolc University Press