<p>In mathematical physics and physical applications, dealing with exact solutions to PDE system, especially for variable-coefficient PDE (vc-PDE) system is an interesting and challenging work. This paper is concerned with the space dependent variable-coefficient carbon nanotubes (vc-CNTs) system, which is of great importance in mechanics, engineering and physical applications. By the combination of Lie symmetry analysis and dynamical system method, all of the point symmetries of the space-dependent PDE system are obtained, the symmetry reductions and exact solutions to the systems are investigated, then the analytic solution to the vc-system is obtained by the analytic method. Furthermore, the generalized symmetries of the systems are provided by the recursion operator method, the explicit solutions generated from the generalized symmetries and generalized separation of variables method (GSVM) are constructed.</p>