OME 1987 Problem 4

If $a$ and $b$ are distinct real numbers, solve the systems (a) $\begin{cases} x+y = 1 (ax+by)^2 \le a^2x+b^2y \end{cases}$ and (b) $\begin{cases} x+y = 1 (ax+by)^4 \le a^4x+b^4y \end{cases}$