Solve system using elimination

[ElaniaA]

System:
x+3y+z=-6
2x+y+3z=-4
-3x-3y-3z=6

Work so far:
-2x-6y-6z=12
2x+y+3z=-4
5y-6z=8

3x+9y+3z=-18
-3x-3y-3z=6
6y=-12
y=-2

5(-2)-6z=8
-10-6z=8
-6z=18
z=-3

-3x-3(-2)-3(-3)=6
-3x+6+9=6
-3x+15=6
-3x=9
x=-3

CHECK:
2(-3)+(-2)+3(-3)=-4
-6-2-9=-4
-8-9=-4
-17=-4 ...well they didn't come out equal so I did something wrong but i can't figure out what :?
It might be really obvious and I just don't see it >.<

 

[Mrspi]

System:
x+3y+z=-6
2x+y+3z=-4
-3x-3y-3z=6

Work so far:
-2x-6y-6z=12<------if this was supposed to be the result of multiplying the first equation by -2, it SHOULD be -2x - 6y - 2z = 12
Now....make this correction and continue
2x+y+3z=-4
5y-6z=8

3x+9y+3z=-18
-3x-3y-3z=6
6y=-12
y=-2

5(-2)-6z=8
-10-6z=8
-6z=18
z=-3

-3x-3(-2)-3(-3)=6
-3x+6+9=6
-3x+15=6
-3x=9
x=-3

CHECK:
2(-3)+(-2)+3(-3)=-4
-6-2-9=-4
-8-9=-4
-17=-4 ...well they didn't come out equal so I did something wrong but i can't figure out what :?
It might be really obvious and I just don't see it >.<

 

[ElaniaA]

thanks for that correction!
continued:
5(-2)+z=8
-10+z=8
z=18

-3(x)-3(-2)-3(18)=6
-3x+6-54=6
-3x+48
-3x=54
x=-18

CHECK:
2(-18)+(-2)+3(18)=-4
-36-2+54=-4
-38+54=-4
16=-4 Another silly mistake somewhere maybe? I'll keep working on it...

 

[ElaniaA]

thanks for that correction!
continued:
5(-2)+z=8
-10+z=8
z=18

-3(x)-3(-2)-3(18)=6
-3x+6-54=6
-3x+48
-3x=54
x=-18

CHECK:
2(-18)+(-2)+3(18)=-4
-36-2+54=-4
-38+54=-4
16=-4 Another silly mistake somewhere maybe? I'll keep working on it...

Oh wait I see!

Oh no..never mind I don't see >.<

 

[mmm4444bot]

continued:

5(-2)+z=8

The equation 5y + z = 8 is not correct.

You made an arithmetic mistake when you added 1 to -6. The result is -5, not 5.

-2x - 6y - 2z = 12
2x + y + 3z = -4

The sum of these two equations is:

-5y + z = 8

If your results continue to fail, double-check all of your arithmetic.