For solving a system of six equations with six variables, a TI-83 calculator is recommended for linear equations. If the equations are non-linear, Computer Algebra Software like Sage can be utilized, though free options are limited. Excel is also a viable alternative for smaller problems, using matrix functions such as MMULT and MINVERSE. Users appreciate the simplicity of these tools for their needs. Overall, while options exist, the choice depends on the nature of the equations involved.