My objective is linear

\(a\) and \(b\) are positive integers such that

\[ \begin{cases} 7b-11a \leq 1000 \\ ab + a^2= 1+b^2. \\ \end{cases} \]

What is the largest possible value of \(7b-11a \)?

Details and assumptions

There is no restriction that \(a\) or \(b\) must be less than 1000.

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