Question 178001
You didn't specify a method. 
Matrix inversion is the fastest.
[A][x]=[B]
where 
[A]={{{(matrix(3,3,2,-3,1,1,3,8,3,-1,2))}}}
[x]={{{(matrix(3,1,x,y,z))}}}
[B]={{{(matrix(3,1,5,22,12))}}}
Find the inverse matrix of A.
[A]inv={{{-(1/48)*(matrix(3,3,14,5,-27,22,1,-15,-10,-7,9))}}}
The solution is then the inverse matrix multiplied by B. 
[x]={A]inv[B]
[x]={{{-(1/48)*(matrix(3,3,14,5,-27,22,1,-15,-10,-7,9))*(matrix(3,1,5,22,12))}}}
[x]={{{(matrix(3,1,3,1,2))}}}