Help with systems of solving equation with three variables

(I will post the question)

Question

Help with systems of solving equation with three variables

(I will post the question)

anonymous · Answer

2x + y - 2z = 3
x- y + z = 3
x+ 3y - 3z = 3

anonymous · Answer

I tried using elimination method by first taking equation 1 and 2, then equation 2 and 3
I got these equations as a result: 
3x - z = 6
-2x - 6z = -6

anonymous · Answer

But when i tried to use elimination for those two equations I ended up with a fraction x= 21/10

thomas5267 · Answer

Nope.  The answers are all in nice integers.

anonymous · Answer

Could someone check my work and tell me where I went wrong?

thomas5267 · Answer

Your second equation is wrong I think.  3 times the second equation is then added to the third one not subtracted.

thomas5267 · Answer

x - y (yes that is a minus y) + z = 3

anonymous · Answer

This is what I did for the second and thrid equation
-3x - 3y -3z = -9 (i multplied this one by -3)
+ x + 3y - 3z =3 
and I got -2x -6z = -6 when I added them

thomas5267 · Answer

$$
x{\color{red}-}y+z=3\
$$