If 2x + y = 15, 2y + z = 25 and 2z + x = 26, what is the value of z?

Question: If 2x + y = 15, 2y + z = 25 and 2z + x = 26, what is the value of z?

Solution:
2x + y = 15..............(1)
2y + z = 25 ..............(2)
2z + x = 26..............(3)

(1) + (2) + (3)⇒
2x + y + 2y + z + 2z + x = 15 + 25 + 26
3x + 3y + 3z = 66
3(x + y + z) = 66
x + y + z = 22..................(4)

From (2)
2y + z = 25
2y = 25 - z
y = (25 - z)/2

From (3)
2z + x = 26
x = 26 - 2z

From (4)
x + y + z = 22
26 - 2z + {(25 - z)/2} + z = 22
52 - 4z + 25 - z + 2z = 44
77 - 3z = 44
- 3z = 44 - 77
- 3z = - 33
z = 11