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: \[\displaystyle \sum_{i=1}^{n} x_i + y_i\]

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