Solving linear system. HELP!!!

First, I am going to eliminate x:

Using the first two equations:

x - 3y + 6z = 21      --->  x -3                  --->     -3x + 9y - 18z = -63

3x + 2y - 5z = -30   --> leaving this alone  --->     3x + 2y - 5z = -30

               Adding down the columns          --->            11y - 23z = -93

Using the first and the third equations:

x - 3y + 6z = 21      --->  x -2                  --->   -2x + 6y - 12z = -42

2x - 5y + 2z = -6    --->  leaving this alone  --->  2x - 5y + 2z = -6

               Adding down the columns           --->           y - 10z = -48

We now have thse two equaitons:

 11y - 23z = -93

y - 10z = -48

Eliminating the y-term:

11y - 23z = -93    --->  leaving this alone  --->  11y - 23z = -93

-y - 10z = -48       -->  x  -11     --->               -11y +110z = +528

               Adding down the columns        --->                87z = 435            --->  z = 5

Substituting z = 5 back into y - 10z = -48   --->   y - 10(5) = -48               --->  y = 2

Substituting z = 5 and y = 2 back into x - 3y + 6z = 21  --->  x - 3(2) + 6(5) = 21   ---> x = -3

I hope that helps!