abx−bay=a+b
a2x−b2y=ab(a+b)
a2x−b2y=a2b+ab2 ........... (1)
second equation is,
ax−by=2ab ...............(2)
Multiply the above equation by a
a2x−aby=2a2b ................(3)
Subtract (3) from (1),
−b2y+aby=a2b+ab2−2a2b
−b2y+aby=−a2b+ab2
b(−b+a)y=−ab(a−b)
by=−ab
y=−a
From equation (1),
ax−by=2ab
ax−b(−a)=2ab
ax=2ab−ab
ax=ab
x=b