[tex]\left\{\begin{matrix}
\sqrt{6} x + \sqrt{2}y = 2 \sqrt{2}(3 + \sqrt{3} ) \\
\sqrt{2}x + \sqrt{3} y = 6 + 2 \sqrt{6} \end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
\sqrt{6} x + \sqrt{2}y = 6 \sqrt{2} + 2 \sqrt{6} \\
\sqrt{2}x + \sqrt{3} y = 6 + 2 \sqrt{6} \: | \times ( - \sqrt{3} ) \end{matrix}\right.[/tex]
[tex]\left\{\begin{matrix}
\sqrt{6} x + \sqrt{2} y = 6 \sqrt{2} + 2 \sqrt{6} \\
- \sqrt{6} x - 3y = - 6 \sqrt{3} - 2 \sqrt{18} \end{matrix}\right.[/tex]
[tex] \sqrt{2} y - 3y = 6 \sqrt{2} + 2 \sqrt{6} - 6 \sqrt{3} - 6 \sqrt{2} [/tex]
[tex] \sqrt{2} y - 3y = 2 \sqrt{6} - 6 \sqrt{3} [/tex]
[tex]y = \frac{2 \sqrt{6} - 6 \sqrt{3} }{ \sqrt{2} - 3 } [/tex]
[tex]y = \frac{( \sqrt{2} + 3)(2 \sqrt{6} - 6 \sqrt{3} )}{2 - 9} [/tex]
[tex]y = - \frac{2 \sqrt{12} - 6 \sqrt{6} + 6 \sqrt{6} - 18 \sqrt{3} }{7} [/tex]
[tex]y = - \frac{4 \sqrt{3} - 18 \sqrt{3} }{7} [/tex]
[tex]y = \frac{14 \sqrt{3} }{7} [/tex]
[tex]y = 2 \sqrt{3} [/tex]
[tex] \sqrt{2} x + \sqrt{3} y = 6 + 2 \sqrt{6} [/tex]
[tex] \sqrt{2} x + 2 \sqrt{3} \times \sqrt{3} = 6 + 2 \sqrt{6} [/tex]
[tex] \sqrt{2} x + 6 = 6 + 2 \sqrt{6} [/tex]
[tex] \sqrt{2} x = 2 \sqrt{6} [/tex]
[tex]x = \frac{2 \sqrt{6} }{ \sqrt{2} } [/tex]
[tex]x = 2 \sqrt{3} [/tex]
