$$5+ \sqrt{ 3 } /7-4 \sqrt{ 3 } =47x+3y$$
$x=-\frac{3y}{47}-\frac{27\sqrt{3}}{329}+\frac{5}{47}$
$$35+\sqrt{3}-28\sqrt{3}=329x+21y$$
$$35-27\sqrt{3}=329x+21y$$
$$329x+21y=35-27\sqrt{3}$$
$$329x=35-27\sqrt{3}-21y$$
$$329x=-21y+35-27\sqrt{3}$$
$$\frac{329x}{329}=\frac{-21y+35-27\sqrt{3}}{329}$$
$$x=\frac{-21y+35-27\sqrt{3}}{329}$$
$$x=-\frac{3y}{47}-\frac{27\sqrt{3}}{329}+\frac{5}{47}$$
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$y=-\frac{47x}{3}-\frac{9\sqrt{3}}{7}+\frac{5}{3}$
$$21y=35-27\sqrt{3}-329x$$
$$21y=-329x+35-27\sqrt{3}$$
$$\frac{21y}{21}=\frac{-329x+35-27\sqrt{3}}{21}$$
$$y=\frac{-329x+35-27\sqrt{3}}{21}$$
$$y=-\frac{47x}{3}-\frac{9\sqrt{3}}{7}+\frac{5}{3}$$
