\(\begin{cases} \sqrt5 x-y=\sqrt5(\sqrt3-1)\\ 2\sqrt3x+3\sqrt5y=21 \end{cases} \\\Leftrightarrow \begin{cases} y=\sqrt5x-\sqrt{3}.\sqrt5+\sqrt5\\ 2\sqrt3x+3\sqrt5(\sqrt5x-\sqrt3.\sqrt5+\sqrt5)=21\end{cases} \\\Leftrightarrow \begin{cases} y=\sqrt5(x-\sqrt3+1)\\ (15+2\sqrt3)x=15\sqrt3+6 \end{cases} \\\Leftrightarrow \begin{cases} y=\sqrt5(\sqrt3-\sqrt3+1)=\sqrt5\\ x=\sqrt3 \end{cases} \)
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\(\left\{{}\begin{matrix}\sqrt{5}x-y=\sqrt{5}\left(\sqrt{3}-1\right)\\2\sqrt{3}x+3\sqrt{5}y=21\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=\sqrt{5}x-\sqrt{5}\left(\sqrt{3}-1\right)=\sqrt{5}x-\sqrt{15}+\sqrt{5}\\2\sqrt{3}x+3\sqrt{5}\left(\sqrt{5}x-\sqrt{15}+\sqrt{5}\right)=21\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=\sqrt{5}x-\sqrt{15}+\sqrt{5}\\2\sqrt{3}x+15x-15\sqrt{3}+15=21\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=\sqrt{5}x-\sqrt{15}+\sqrt{5}\\2\sqrt{3}x+15x=6+15\sqrt{3}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=\sqrt{5}x-\sqrt{15}+\sqrt{5}\\x=\dfrac{6+15\sqrt{3}}{2\sqrt{3}+15}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=\sqrt{5}\cdot\sqrt{3}-\sqrt{15}+\sqrt{5}\\x=\sqrt{3}\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}y=\sqrt{5}\\x=\sqrt{3}\end{matrix}\right.\)
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