2 equations, 3 variables!

Algebra Level 4

\[ \large { \begin{cases}a-7b+8c=4 \\ 8a+4b-c=7 \end{cases} } \]

Let \(a,b\) and \(c\) be real numbers satisfying the system of equations above. Find the value of \(60(a^2-b^2+c^2) \).

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