Question 15
Find $ax^5+by^5$ if the real numbers $a,$ $b,$ $x,$ and $y$ satisfy the equations $$
\begin{aligned}ax+by&=3,\\ax^2+by^2&=7,\\ax^3+by^3&=16,\\ax^4+by^4&=42.\end{aligned}
$$
\begin{aligned}ax+by&=3,\\ax^2+by^2&=7,\\ax^3+by^3&=16,\\ax^4+by^4&=42.\end{aligned}
$$