29: \(\left\{{}\begin{matrix}5x\sqrt{3}+y=2\sqrt{2}\\x\sqrt{6}-y\sqrt{2}=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}5x\sqrt{6}+y\sqrt{2}=4\\x\sqrt{6}-y\sqrt{2}=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}6x\sqrt{6}=6\\x\sqrt{6}-y\sqrt{2}=2\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{1}{\sqrt{6}}=\dfrac{\sqrt{6}}{6}\\y\sqrt{2}=x\sqrt{6}-2=\sqrt{6}\cdot\dfrac{\sqrt{6}}{6}-2=1-2=-1\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=\dfrac{\sqrt{6}}{6}\\y=-\dfrac{\sqrt{2}}{2}\end{matrix}\right.\)
30: \(\left\{{}\begin{matrix}0,2x+0,1y=0,3\\3x+y=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+y=3\\3x+y=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+y-3x-y=3-5\\3x+y=5\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}-x=-2\\y=5-3x\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=2\\y=5-3\cdot2=-1\end{matrix}\right.\)
31: \(\left\{{}\begin{matrix}0,75x-3,2y=10\\x\sqrt{3}-y\sqrt{2}=4\sqrt{3}\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x-\dfrac{y\sqrt{6}}{3}=4\\x-\dfrac{64}{15}y=\dfrac{40}{3}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y\left(-\dfrac{\sqrt{6}}{3}+\dfrac{64}{15}\right)=4-\dfrac{40}{3}\\x-\dfrac{y\sqrt{6}}{3}=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=-\dfrac{28}{3}:\dfrac{-5\sqrt{6}+64}{15}=\dfrac{-28}{3}\cdot\dfrac{15}{64-5\sqrt{6}}=\dfrac{-140}{64-5\sqrt{6}}\\x=4+\dfrac{y\sqrt{6}}{3}=4+\dfrac{-140}{64-5\sqrt{6}}\cdot\dfrac{\sqrt{6}}{3}=\dfrac{12\left(64-5\sqrt{6}\right)-140\sqrt{6}}{3\left(64-5\sqrt{6}\right)}\end{matrix}\right.\)
32: \(\left\{{}\begin{matrix}2x+y=7\\-x+4y=10\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}2x+y=7\\-2x+8y=20\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}9y=27\\2x+y=7\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}y=3\\2x=7-y=7-3=4\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}x=2\\y=3\end{matrix}\right.\)
