Answer
See below.
Work Step by Step
As we can see the second equation doesn't contain the variable $z$. To get one more equation without $z$, we could add the first and third equations because then $z$ and $-z$ "cancel" each other because then we get the equation: $(x+y+z)+(10y-z)=2+12\\x+(y+10y)+(z-z)=14\\x+11x=14$
