To solve this system of equations, we can use the method of substitution or elimination.

Given equations:
1) 2x + y = 91
2) x + 2y = 62
3) y - 2z = 9

First, let's solve equations 1 and 2 using the method of elimination:
Multiply equation 2 by 2:
4) 2(x + 2y) = 2(62)
2x + 4y = 124

Subtract equation 1 from equation 4 to eliminate x:
2x + 4y - 2x - y = 124 - 91
3y = 33
y = 33 / 3
y = 11

Now, substitute y = 11 into equation 1 to solve for x:
2x + 11 = 91
2x = 91 - 11
2x = 80
x = 80 / 2
x = 40

Now that we have found x = 40 and y = 11, we can substitute them into equation 3 to solve for z:
11 - 2z = 9
-2z = 9 - 11
-2z = -2
z = -2 / -2
z = 1

Therefore, x = 40, y = 11, and z = 1.