DE-MO 1996 Problem 2

Let $a$ and $b$ be positive real numbers smaller than $1$ . Prove that the following two statements are equivalent: (i) $a+b = 1$ , (ii) Whenever $x,y$ are positive real numbers such that $x < 1, y < 1, ax+by < 1$ , the following inequlity holds: $$\frac{1}{1-ax-by} \le \frac{a}{1-x} + \frac{b}{1-y}$$