An algebra problem by Djordje Veljkovic

Algebra Level 5

{x2+3xy=54xy+4y2=115 \begin{cases} x^2 + 3xy= 54 \\ xy + 4y^2= 115 \end{cases}

If all the ordered pairs of reals (x,y)(x,y) satisfying the system of equations above are (x1,y1),(x2,y2),(x3,y3),(x4,y4),(x_1, y_1), (x_2, y_2), (x_3, y_3), (x_4, y_4), find x1y1+x2y2+x3y3+x4y4x_1y_1 + x_2 y_2 + x_3 y_3 + x_4 y_4.

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