Nothing Special

Algebra Level 2

$\large \begin{cases} a + b + c + d = 14 \\ a + b + c + e = 15 \\ a + b + d + e = 17 \\ a + c + d + e = 18 \\ b + c + d + e = 20\end{cases}$

If $$a,b,c,d$$ and $$e$$ satisfy the system of equations above, find the product $$abcde$$.

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