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$\large \begin{cases} \dfrac{dv}{dt} = 4v - 5w \\ \dfrac{dw}{dt} = 2v - 3w \end{cases}$

Solve the system of differential equations above. Given that $v(0) = 8$ and $w(0) = 5$, evaluate $\left \lfloor v(1) - w(1) \right \rfloor$

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