Step 1 :First, we use Gaussian elimination method to solve the system of linear equations with three variables x, y, and z.
Step 2 :After solving the system, we get the final answer: \(x = 2\), \(y = -4\), and \(z = -6\).
Step 3 :\(\boxed{x = 2, y = -4, z = -6}\)