\(\left\{{}\begin{matrix}3\sqrt{5}\cdot x-4y=15-2\sqrt{7}\\-2\sqrt{5}x+8\sqrt{7}y=18\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x\cdot6\sqrt{5}-8y=30-4\sqrt{7}\\x\cdot\left(-6\sqrt{5}\right)+24\sqrt{7}\cdot y=54\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y\left(24\sqrt{7}-8\right)=54+30-4\sqrt{7}=84-4\sqrt{7}\\3\sqrt{5}\cdot x-4y=15-2\sqrt{7}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=\dfrac{84-4\sqrt{7}}{24\sqrt{7}-8}=\dfrac{21-\sqrt{7}}{6\sqrt{7}-2}=\dfrac{\sqrt{7}}{2}\\x\cdot3\sqrt{5}=4y+15-2\sqrt{7}=15-2\sqrt{7}+2\sqrt{7}=15\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=\dfrac{\sqrt{7}}{2}\\x=\sqrt{5}\end{matrix}\right.\)
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