We show that the following class of two-dimensional hyperbolic-cotangent-type systems of difference equations
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\begin{document}$$ x_{n+1}=\frac{u_{n-k}v_{n-l}+a}{u_{n-k}+v_{n-l}},\quad \quad y_{n+1}= \frac{w _{n-k}s_{n-l}+a}{w_{n-k}+s_{n-l}},\quad n\in {\mathbb {N}} _{0}, $$\end{document} where k,l∈N0\documentclass[12pt]{minimal}
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\begin{document}$k,l\in {\mathbb {N}} _{0}$\end{document}, a∈C\documentclass[12pt]{minimal}
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\begin{document}$u_{-j}, w_{-j}\in {\mathbb {C}} $\end{document}, j=1,k‾\documentclass[12pt]{minimal}
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\begin{document}$j=\overline{1,k}$\end{document}, v−j′\documentclass[12pt]{minimal}
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\begin{document}$j'=\overline{1,l}$\end{document}, and each of the sequences un\documentclass[12pt]{minimal}
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\begin{document}$u_{n}$\end{document}, vn\documentclass[12pt]{minimal}
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\begin{document}$w_{n}$\end{document}, sn\documentclass[12pt]{minimal}
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\begin{document}$s_{n}$\end{document} is equal to xn\documentclass[12pt]{minimal}
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\begin{document}$x_{n}$\end{document} or yn\documentclass[12pt]{minimal}
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\begin{document}$y_{n}$\end{document}, is theoretically solvable. When k=0\documentclass[12pt]{minimal}
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\begin{document}$l=1$\end{document}, 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.
