This equation is ambiguous. Let's take (2/x)-5y+1=0, (2/x)-y+3=0 first. From the first equation 2/x=5y-1. From the second equation 2/x=y-3, so:
5y-1=y-3, 4y=-2, y=-½, so 2/x=y-3=-7/2, making x=2/(-7/2)=-4/7.
Now let's take 2/(x-5y)+1=0, 2/(x-y)+3=0.
So 2+x-5y=0 and 2+3(x-y)=0, 2+3x-3y=0
x-5y=-2 and 3x-3y=-2.
Multiply the first equation by -3: -3x+15y=6 and add to the second equation:
12y=4, y=⅓. x-5y=-2 so x-5/3=-2, x=5/3-2=(5-6)/3=-⅓.
Depending on the interpretation the answer is x=-4/7, y=-½; or x=-⅓, y=⅓.