On a system of difference equations of odd order solvable in closed form

It is shown that the next system of difference equationsxn=cnyn-(2k-1)an+bnyn-(2k-1)∏i=1k-1yn-(2i-1)xn-2i,yn=γnxn-(2k-1)αn+βnxn-(2k-1)∏i=1k-1xn-(2i-1)yn-2in∈N0, where an,bn,cn,αn,βn,γn, n∈N0, and initial values x-i,y-i, i∈{1,2,…,2k-1} are real numbers, is solved in closed form, and the behavior of its well-defined solutions when all the coefficients in the system are constant is described.