In this paper we solve the following system of difference equations xn+1 = zn−1 a + bynzn−1 , yn+1 = xn−1 a + bznxn−1 , zn+1 = yn−1 a + bxnyn−1 , n ∈ N0 where parameters a, b and initial values x−1, x0, y−1, y0, z−1, z0 are nonzero real numbers, and give a representation of its general solution in terms of a specially chosen solutions to homogeneous linear difference equation with constant coefficients associated to the system.

In this paper we represent the well-defined solutions of the system of the higher-order rational difference equationsin terms of Fibonacci and Lucas sequences, where the initial valuesdo not equal -3. Some theoretical explanations related to the representation for the general solution are also given.