In this paper, we investigate two-dimensional system of difference equations with variable coefficients. Firstly, we obtain the general solutions of mentioned system of difference equations. Later, the solutions of this system of difference equations are acquired when the coefficients are constant. Additionally, the solutions are expressed when the parameters α and γ are equal to 1 or not equal to 1. Further, we research the asymptotic behavior of the well-defined solutions of aforementioned system of difference equations. Lastly, the forbidden set of the initial conditions is acquired by using obtained formulas.
Dilbeyen et al. (Wed,) studied this question.