Most beautiful problem

Algebra Level 5

\[ \large \begin{cases} x+\dfrac{3x-y}{x^2+y^2} &=& 3 \\ y- \dfrac{x+3y}{x^2+y^2}&=&0 \end{cases} \]

Solve the system of equations for real values of \((x,y)\), and submit the sum of all values of \((x,y)\).

ie. If you have got pairs as \((9,10),(5,7)\) submit your answer as \(9+10+5+7\).

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