| Summary: | Abstract We show that the following class of two-dimensional hyperbolic-cotangent-type systems of difference equations xn+1=un−kvn−l+aun−k+vn−l,yn+1=wn−ksn−l+awn−k+sn−l,n∈N0, $$ x_{n+1}=\frac{u_{n-k}v_{n-l}+a}{u_{n-k}+v_{n-l}},\quad \quad y_{n+1}= \frac{w _{n-k}s_{n-l}+a}{w_{n-k}+s_{n-l}},\quad n\in {\mathbb {N}} _{0}, $$ where k,l∈N0 $k,l\in {\mathbb {N}} _{0}$, a∈C $a\in {\mathbb {C}} $, u−j,w−j∈C $u_{-j}, w_{-j}\in {\mathbb {C}} $, j=1,k‾ $j=\overline{1,k}$, v−j′ $v_{-j'}$, s−j′ $s_{-j'}$, j′=1,l‾ $j'=\overline{1,l}$, and each of the sequences un $u_{n}$, vn $v_{n}$, wn $w_{n}$, sn $s_{n}$ is equal to xn $x_{n}$ or yn $y_{n}$, is theoretically solvable. When k=0 $k=0$ and l=1 $l=1$, we show that the systems are practically solvable by presenting closed-form formulas for their solutions. To do this, we employ a constructive method, which is possible to use on the complex domain, presenting in this way a new and elegant solution to the problem in this case, and giving a hint how such type of systems can be solved.
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