On a solvable system of difference equations of fourth order

The system of difference equationsxn=cnxn-4an+bnyn-1xn-2yn-3xn-4,yn=γnyn-4αn+βnxn-1yn-2xn-3yn-4,n∈N0n∈N0, where the sequences an,bn,cn,αn,βn,γn,n∈N0an,bn,cn,αn,βn,γn,n∈N0, and initial values x-i,y-i,i∈{1,2,3,4}x-i,y-i,i∈{1,2,3,4} are real numbers, such that cn≠0,γn≠0,n∈N0, is solved in closed form, and based on the obtained formulae is studied the asymptotic behaviour of well-defined solutions of the system.