on the system of difference equations xn = xn−2yn−3 / yn−1(an+bnxn−2yn−3), yn = yn−2xn−3 / xn−1(αn+βnyn−2xn−3)

In this paper, we show that the system of difference equations xn = xn−2yn−3 / yn−1 (an + bnxn−2yn−3) , yn = yn−2xn−3 / xn−1 (αn + βnyn−2xn−3) , n ∈ n0, where the sequences ∀n ∈ n0, (an) , (bn) , (αn) , (βn) and the initial values x−j , y−j , j ∈ {1, 2, 3} are non-zero real numbers, can be solved in the closed form. for the case when all the sequences (an) , (bn) , (αn) , (βn) are constant we describe the asymptotic behavior and periodicity of solutions of above system is also investigated