If $x+y+z=9,x+2y+3z=20$ and $x+3y+6z=35$, then $z$ equals:

Subtracting the first equation from the second gives $y+2z=11$; subtracting the second from the third gives $y+3z=15$. So $z=4$, then $y=3$ and $x=2$. Check in the third equation: 2 + 9 + 24 = 35.