There are several other categories. Nonlinear models may include polynomial expressions, differential equations, exponents, logarithms, trigonometric functions, and other functions in variables and coefficients. Mixed integer programming involves models with decision variables and constraints that may be limited to integer values. In integer programming, a special case, all decision variables and constraints are integers. Variations of integer programming, in which variable values are limited to finite sets, are widely used in network design, planning, scheduling, and routing.
Complementarity problems force equality on one of the constraints.
Finally, stochastic models include error or uncertainty terms defined by probability distributions. The next steps are to code the model and choose the solver. Several excellent software tools exist that solve a variety of simultaneous-equation models. If your problem is small, use the solver available in your spreadsheet program, since you're already familiar with the spreadsheet interface. But if you have a larger problem and you're not forced to use a particular solver, choose one that includes or can be associated with a declarative modeling language featuring algebraic constraint and computational statements.