Cool Exponential Algebraic!

Algebra Level 3

Find the value of \(ax^5+by^5\) if the real numbers a, b, x and y satisfy the system of equations

\(ax+by=3\)

\(ax^2+by^2=7\)

\(ax^3+by^3=16\)

\(ax^4+by^5=42\)

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