System of equation with 3 variables

The teacher said the answer is (1,2,-4) but i don't understand how and he gave out the answer as the bell rang. Heres the problem

-x-6y-z=-9
x+6y+2z=5
x-6y-2z=-3

I can get one new equation using the first and third but the rest i get 2 variables that cancel out.

-x-6y-z=-9
x+6y+2z=5
---------------
0+0 +z = -4

z= -4

x+6y+2z=5
x-6y-2z=-3
----------------
2x+0+0 = 2

2x=2
x=2/2
x=1

x+6y+2z=5
6y = 5 - x - 2z
6y = 5 - 1 - 2(-4)
6y = 4 + 8
6y = 12
y = 12/6
y= 2