LAUSR

In this paper we show that the system of difference equations  $$ x_{n}=ay_{n-k}+\frac{dy_{n-k}x_{n-\left( k+l\right) }}{bx_{n-\left( k+l\right) }+cy_{n-l}},\ y_{n}=\alpha x_{n-k}+\frac{\delta x_{n-k}y_{n-\left( k+l\right) }}{\beta y_{n-\left( k+l\right) }+\gamma x_{n-l}},$$ where $n\in \mathbb{N}_{0},$ $k$ and $l$ are fixed naturel numbers, the parameters $a$, $b$, $c$, $d $, $\alpha $, $\beta $, $\gamma $, $\delta $ are real numbers and the initial values $x_{-j}$, $y_{-j}$, $j=\overline{1,k+l}$, are real numbers, can be solved in the closed form. Also, we determine the asymptotic behavior of solutions for the case $l=1$ and describe the forbidden set of the initial values using the obtained formulae. Our obtained results significantly extend and develop some recent results in the literature.