Let's solve the system of equations step by step:

Simplify the first equation:
2(x + y) - x - 6 = 0
2x + 2y - x - 6 = 0
x + 2y - 6 = 0
x = 6 - 2y

Substitute the value of x into the second equation:
3x - (x - y) = 0
3(6 - 2y) - (6 - 2y - y) = 0
18 - 6y - 6 + 2y = 0
12 - 4y = 0
4y = 12
y = 3

Substitute the value of y back into the first equation:
x = 6 - 2(3)
x = 6 - 6
x = 0

Check the values in the third equation:
(x + 5y = -2.5)
(0 + 5(3)) = -2.5
0 + 15 = -2.5
15 = -2.5 (not true)

Therefore, the system of equations is inconsistent and does not have a solution.