\(\left\{{}\begin{matrix}x-y+z=5\\6x-2y+3z=4\\-2x+3y-5z=-10\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}6x-6y+6z=30\\6x-2y+3z=4\\-6x+6y-10z=-20\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}-6y+6z+2y-3z=26\\6x-6y+6z-6x+6y-10z=10\\x-y+z=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-4y+3z=26\\-4z=10\\x-y+z=5\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}z=-\dfrac{5}{2}\\4y=3z-26=3\cdot\dfrac{-5}{2}-26=-\dfrac{67}{2}\\x-y+z=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}z=-\dfrac{5}{2}\\y=-\dfrac{67}{8}\\x=5+y-z=-\dfrac{7}{8}\end{matrix}\right.\)
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