More info:

The article is an introduction to Constraint Satisfaction Problems (CSP's). http://en.wikipedia.org/wiki/Constraint_satisfaction_problem

A very rudimentary demonstration of this: http://aispace.org/constraint/sample2.html

Norvig implemented a quick and dirty version of this for his sudoku solver: http://norvig.com/sudoku.html.

Note, while you eventually end up just telling a CSP what you want, there's a plethora of algorithms to solve these constraints.

I think the example cheats a lot by assuming the solutions have to be positive integers. Is there a mechanism to tell the system "a and b are integers", and if so, could the system still solve the simultaneous equation?

About solving systems of simultaneous equations, I don't know if this particular solver can do it but many solvers can by using Gaussian Elimination from linear algebra.

http://en.wikipedia.org/wiki/Gaussian_elimination

This is basically logic programming. If you really want to do something like this, you are far better off just using a logic language like prolog and saving yourself the trouble.