# Problem of the year 2016

Algebra Level 5

\begin{align} ax + by & = 3 \\ a{ x }^{ 2 } + b{ y }^{ 2 } & = 7 \\ a{ x }^{ 3 } + b{ y }^{ 3 } & = 16 \\ a{ x }^{ 4 } + b{ y }^{ 4 } & = 42 \end{align}.

If $$a$$, $$b$$, $$x$$, and $$y$$ are real numbers satisfying the system of equations above, find $$a{ x }^{ 5 } + b{ y }^{ 5 }$$.

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