You may not have studied the augmented matrix method yet. Here's how to
solve it by elimination:

1.  Pick a letter to eliminate.
2.  Eliminate that letter from any two of the 3 equations that contain 
    that letter.
3.  Eliminate the SAME letter for one of those equations you just used but
    this time using the third equation.
4.  Now you have a new system of only two equations in two unknowns.
5.  Solve this system for those two unknowns.
6.  Substitute those values in one of the original equations to find the
    remaining letter.  [It will be the first letter eliminated.    




Add the first and third equations term by term to eliminate x

 x +  y +  z =   9
-x + 8y - 3z = -39
------------------
     9y - 2z = -30

Now eliminate x from the 2nd and 3rd equations

 2x + 4y + 2z =  14
 -x + 8y - 3z = -39

To make the x's cancel we must multiply the second one
above through by 2


 2x +  4y + 2z =  14
-2x + 16y - 6z = -78
--------------------
      20y - 4z = -64

We can simplify that by dividing through by 4

      5y -  z = -16

Now we have this system which is 2 equations and 2 unknowns.



To make the z's cancel we must multiply the second one
above through by -2

  9y - 2z = -30
-10y + 2z =  32
---------------
  -y      =   2

Divide both sides by -1

        y = -2

Substitute -2 for y in

      5y -  z = -16
    5(-2) - z = -16
      -10 - z = -16
           -z = -6
            z = 6

Substitute both y = -2 and z = 6 in one
of the original equations:

    x + y + z = 9 
 x + (-2) + 6 = 9
    x - 2 + 6 = 9
        x + 4 = 9
            x = 5

Solution (x,y,z) = (5,-2,6)

Edwin