Find all solution in $\mathbb{R}$ for the following system of equations:

$\{\begin{array}{l}x+\frac{3x-y}{{x}^{2}+{y}^{2}}=3\\ y\u2013\frac{x+3y}{{x}^{2}+{y}^{2}}=0\end{array}$

$\{\begin{array}{l}x+\frac{3x-y}{{x}^{2}+{y}^{2}}=3\\ y\u2013\frac{x+3y}{{x}^{2}+{y}^{2}}=0\end{array}$