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 \(a+b+c\).