First of all, we can simply the first and second equations by [tex] 2 [/tex] and [tex] 3 [/tex], respectively, to get
[tex] x+y+2z=12 [/tex]
[tex] 2x+y=5 [/tex]
[tex] y+2z=11 [/tex]
If we subtract the third equation from the first, we already figure out that [tex] x=1 [/tex]. The system becomes
[tex] y+2z=11 [/tex]
[tex] y=3 [/tex]
[tex] y+2z=11 [/tex]
so we know [tex] y=3 [/tex] as well. Let's plug the values for [tex] x [/tex] and [tex] y [/tex] in any of the three equations to get
[tex] y+2z=11 \iff 3+2z=11 \iff 2z=8 \iff z=4 [/tex]
So, the solution is [tex] x=1 [/tex], [tex] y=3 [/tex], [tex] z=4 [/tex]
