On a solvable system of difference equations of higher-order with period two coefficients

We show that the next difference equations system xₙ₊₁=((aₙxₙ₋ₖ₊₁yₙ₋ₖ)/(yₙ-αₙ))+βₙ₊₁, yₙ₊₁=((bₙyₙ₋ₖ₊₁xₙ₋ₖ)/(xₙ-βₙ))+αₙ₊₁, n∈N₀, where N₀=N∪{0}, the sequences (aₙ)n∈N₀, (bₙ)n∈N₀, (αₙ)n∈N₀, (βₙ)n∈N₀ are two periodic and the initial conditions x₋ᵢ, y₋ᵢ i∈{0,1,…,k}, are non-zero real numbers, can be solved. Also, we investigate the behavior of solutions of above mentioned system when a₀=b₁ and a₁=b₀.