Solvability of two-dimensional system of difference equations with constant coefficients

In the present paper, the solutions of the following system of difference equations {equation*} uₙ=α₁vₙ₋₂+{δ₁vₙ₋₂uₙ₋₄}{β₁uₙ₋₄+γ₁vₙ₋₆}, \ vₙ=α₂uₙ₋₂+{δ₂uₙ₋₂vₙ₋₄}{β₂vₙ₋₄+γ₂uₙ₋₆}, \ n∈ N₀, {equation*} where the initial values u₋ₗ, v₋ₗ, for l=1,6̄ and the parameters αₚ, βₚ, γₚ, δₚ, for p∈\1,2\ are non-zero real numbers, are investigated. In addition, the solutions of aforementioned system of difference equations are presented by utilizing Fibonacci sequence when the parameters are equal $1$. Finally, the periodic solutions according to some special cases of the parameters are obtained.