Do you see a pattern

Algebra Level 3

\begin{align*} a + 4b + 9c &= 3 \\ 4a + 9b + 16c &= 5 \\ 9a + 16b + 25c &= 7 \\ \end{align*}

If $$a,b,c$$ are real numbers satisfying the above system, determine the value of $$a+b+c$$.

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