x = 7y
x + y + z = 80
2x - y + z = 105 → z = 105 - 2x + y (3)
Subbing the first equation into the second, we have
7y + y + z = 80 → 8y + z = 80 (4)
And subbing the first into (3) we have
z = 105 - 2(7y) + y
z = 105 - 13y (5)
Put (5) into (4)
8y + 105 - 13y = 80
-5y = -25 → y = 5
And z = 105 - 13(5) = 105 - 65 = 40
And x = 7y = 7(5) = 35
So (x, y, z) = (35, 5, 40)
