Two broad (and conceptually similar) approaches:

1. Gaussian Elimination.

2. Treat this as a 4x4 matrix acting on a 4D vector to give another vector. Find the inverse of the matrix and apply it to the column vector (18,6,5,11) from the left. The result is your original vector (w,x,y,z). If it's not possible to invert the matrix for whatever reason then the best you can do is find z in terms of w, x, and y. The Gauss-Jordan algorithm can help you there but you'd be no better off than doing option 1.