Think Outside the Box

Algebra Level 4

Let (x1,y1),(x2,y2),,(xn,yn)(x_1, y_1), (x_2, y_2), \dots, (x_n , y_n) be the real solutions to the system of equations

x+3xyx2+y2=3yx+3yx2+y2=0x+\dfrac{3x-y}{x^2 + y^2} =3 \\ y- \dfrac{x+3y}{x^2 + y^2}=0

Evaluate: i=1nxi+yi\displaystyle \sum_{i=1}^{n} x_i + y_i

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