0  -1  -2  -3   1   0   0   0
 1   1   4   4   0   1   0   0
 1   3   7   9   0   0   1   0
-1  -2  -4  -6   0   0   0   1
---------------------------------
 1   1   4   4   0   1   0   0
 0  -1  -2  -3   1   0   0   0
 1   3   7   9   0   0   1   0
-1  -2  -4  -6   0   0   0   1
---------------------------------
 1   1   4   4   0   1   0   0
 0  -1  -2  -3   1   0   0   0
 0   2   3   5   0  -1   1   0
 0  -1   0  -2   0   1   0   1
--------------------------------- 
 1   1   4   4   0   1   0   0
 0   1   2   3  -1   0   0   0
 0   0  -1  -1   2  -1   1   0
 0   0   2   1  -1   1   0   1
--------------------------------- 
 1   1   4   4   0   1   0   0
 0   1   2   3  -1   0   0   0
 0   0   1   1  -2   1  -1   0
 0   0   0  -1   3  -1   2   1
---------------------------------
 1   1   4   4   0   1   0   0
 0   1   2   3  -1   0   0   0
 0   0   1   1  -2   1  -1   0
 0   0   0   1  -3   1  -2  -1
---------------------------------
 1   1   4   0  12  -3   8   4
 0   1   2   0   8  -3   6   3
 0   0   1   0   1   0   1   1
 0   0   0   1  -3   1  -2  -1
---------------------------------
 1   1   0   0   8  -3   4   0
 0   1   0   0   6  -3   4   1
 0   0   1   0   1   0   1   1
 0   0   0   1  -3   1  -2  -1
---------------------------------
 1   0   0   0   2   0   0  -1
 0   1   0   0   6  -3   4   1
 0   0   1   0   1   0   1   1
 0   0   0   1  -3   1  -2  -1
---------------------------------
So the inverse matrix is:
  2   0   0  -1                                                  2
  6  -3   4   1              and multiplying it with the rhs 	 5
  1   0   1   1							-1
 -3   1  -2  -1							 3

produces the column vector
 1
-4
 4
-2     So the solution is:   w=1, x=-4, y=4, z=-2