$\left \{ {{2x+2\sqrt{3}y=1} \atop {\sqrt{3}x+2y=-5}} \right.$
⇔$\left \{ {{2x+2\sqrt{3}y=1} \atop {3x+2\sqrt{3}y=-5\sqrt{3}}} \right.$
⇔$\left \{ {{2x+2\sqrt{3}y=1} \atop {-x=1+5\sqrt{3}}} \right.$
⇔$\left \{ {{y=\frac{1-2x}{2\sqrt{3}} } \atop {x=-1-5\sqrt{3}}} \right.$
⇔$\left \{ {{x=-1-5\sqrt{3}} \atop {y=\frac{10+\sqrt{3}}{2}}} \right.$