Luckily

Algebra Level 4

$\begin{cases} a+2b+3c=13 \\ a^2+4b^2+9c^2 + 3a-2b+15c=82 \end{cases}$

Given that $$a,b$$ and $$c$$ are real numbers with $$a\geq b \geq c$$ and they satisfy the system of equations above, find the value of $$a$$.

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