Think Outside the Box

Algebra Level 4

Let $(x_1, y_1), (x_2, y_2), \dots, (x_n , y_n)$ be the real solutions to the system of equations

$x+\dfrac{3x-y}{x^2 + y^2} =3 \\ y- \dfrac{x+3y}{x^2 + y^2}=0$

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