Another alternative would be to use Math::Symbolic to solve certain classes of equations. The manual of Math::Symbolic::MiscAlgebra has the following on it:

  linear_solve
     Calculates the solutions x (vector) of a linear
     equation system of the form "Ax = b" with "A"
     being a matrix, "b" a vector and the solution "x"
     a vector. Due to implementation limitations, "A"
     must be a quadratic matrix and "b" must have a
     dimension that is equivalent to that of "A".
     Furthermore, the determinant of "A" must be
     non-zero. The algorithm used is devised from
     Cramer's Rule and thus inefficient. The preferred
     algorithm for this task is Gaussian Elimination.
     If you have a matrix and a vector of real numbers,
     please consider using either Math::MatrixReal or
     Math::Pari instead.
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Note that the complexity of Cramer's rule is O(n!) whereas Gaussian Elimination works in O(n^3) as noted by others in this thread.

Steffen