On a system of second-order difference equations

Abstract: We obtain explicit formulas for the solutions of the system of second-order difference equations of the form $x_{n+ 1} = \frac{x_n y_{n-1}}{y_n (a_n + b_n x_n y_{n - 1})}, \quad y_{n+1} = \frac{x_{n - 1} y_n}{x_n (c_n+d_n x_{n-1} y_n)}$, where $(a_n){n\in \mathbb{N}_0},\; (b_n){n\in \mathbb{N}0}, \;(c_n){n\in \mathbb{N}0}$ and $(d_n){n\in \mathbb{N}_0}$ are real sequences. We use Lie symmetry analysis to derive non-trivial symmetries and thereafter, exact solutions are obtained.