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$\begin{cases} x^2 + 3xy= 54 \\ xy + 4y^2= 115 \end{cases}$

If all the ordered pairs of reals $(x,y)$ satisfying the system of equations above are $(x_1, y_1), (x_2, y_2), (x_3, y_3), (x_4, y_4),$ find $x_1y_1 + x_2 y_2 + x_3 y_3 + x_4 y_4$.

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