Gaussian elimination is a method for solving matrix equations/solving systems of linear equations of the form Ax=b.
Solves a system of equations by composing an augmented matrix equation: See Gaussian Elimination - Wikipedia and Gaussian Elimination - Wolfram Alpha for more information on implementing.
Edit math.php, and modify the sample matrix values below:
$A = array(array(2, 4), array(1, 1));
$x = array(8, 2);
$gaus = new Gaussian();
$answer = $gaus->solve($A, $x); // returns [0, 2]