Example Problem Solutions

1.

 x + 2y + 5z = -1
4x - 2y + 2z =  4
       5x + 7z =  3

-2x -  4y - 10z =   2
 3x + 4y -   4z = 14
         x  - 14z = 16

10x + 14z =  6
   x  - 14z = 16
         11x = 22
             x = 2
             z = -1
             y = 1

2.

 x  - 6y  - 2z = -8
-x + 5y + 3z =  2
       -y +   z = -6

-3x + 18y + 6z = 24
 3x  -   2y  - 4z = 18
         16y + 2z = 42

           8y +  z  = 21
             y  -  z  =  6
                   9y = 27
                     y = 3
                     z = -3
                     x = 4

3.

-10x + 6y + 2z = -30
 10x + 2y + 8z =  18
         8y + 10z = -12
         4y +   5z =  -6

-15x + 9y + 3z = -45
 15x + 5y + 7z =   9
       14y + 10z = -36
         7y +  5z = -18

         7y + 5z = -18
         -4y - 5z =   6
                3y = -12
                  y =  -4
                  z =   2
                  x =   1