\left\{ \begin{array} { l } { 3 \sqrt { 7 x } - y = 2 - \frac { \sqrt { 3 } } { 2 } } \\ { \sqrt { 7 x } + \sqrt { 3 y } = 2 - \sqrt { \frac { 3 } { 2 } } } \end{array} \right.
Solve for x, y
x=\frac{-\left(13\sqrt{3}-3\sqrt{2}\right)\sqrt{2\sqrt{3}+43-6\sqrt{6}}+3\sqrt{3}+152-22\sqrt{6}}{14}\approx 0.022191325
y=\frac{-3\sqrt{3\left(2\sqrt{3}+43-6\sqrt{6}\right)}+\sqrt{3}+35-3\sqrt{6}}{2}\approx 0.048418524
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