$\left \{ {{\sqrt[]{7}x+3\sqrt[]{11}y=18} \atop {3\sqrt[]{7}x-\sqrt[]{11}y=\frac{52}{3}}} \right.$
⇔ $\left \{ {{\sqrt[]{7}x+3\sqrt[]{11}y=18} \atop {9\sqrt[]{7}x-3\sqrt[]{11}y=52}} \right.$
⇔ $\left \{ {{10\sqrt[]{7}x=70} \atop {\sqrt[]{7}x+3\sqrt[]{11}y=18}} \right.$
⇔ $\left \{ {{x=\sqrt[]{7}} \atop {\sqrt[]{7}.\sqrt[]{7}+3\sqrt[]{11}y=18}} \right.$
⇔ $\left \{ {{x=\sqrt[]{7}} \atop {7+3\sqrt[]{11}y=18}} \right.$
⇔ $\left \{ {{x=\sqrt[]{7}} \atop {y=\frac{\sqrt[]{11}}{3}}} \right.$
Vậy hệ có nghiệm duy nhất $(x;y)=(\sqrt[]{7};\frac{\sqrt[]{11}}{3})$
