An algebra problem by Djordje Veljkovic

Algebra Level 5

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

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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