1) 27x - 13y = 0
2) 3x - y = 4y/9
Multiply each side by 9: 27x - 9y = 4y
Subtract 4y from both sides: 27x - 13y = 0
This is the same equation as equation1).
3) 9x - 4y = y/3
Multiply each side by 3: 27x - 12y = y
Subtract y from both sides: 27x - 13y = 0
This, also, is the same equation as equation 1).
4) 27x - 12y = y
Subtract y from both sides: 27x - 13y = 0
This, also, is the same equation as equation 1).
There are an infinite number of solutions to 27x - 13y = 0.
Two are: (0, 0) and (13, 27).