\(\left\{{}\begin{matrix}x+y=12\\y+z=-16\\z+x=8\end{matrix}\right.\)
\(\Rightarrow\left(x+y\right)+\left(y+z\right)+\left(z+x\right)=12+\left(-16\right)+8\)
\(\Rightarrow x+y+y+z+z+x=4\)
\(\Rightarrow2\left(x+y+z\right)=4\)
\(\Rightarrow x+y+z=2\)
\(\Rightarrow\left\{{}\begin{matrix}z=2-12=-10\\x=2-\left(-16\right)=18\\y=2-8=-6\end{matrix}\right.\)
Từ \(\left\{{}\begin{matrix}x+y=12\\y+z=-16\\x+z=8\end{matrix}\right.\)\(\Rightarrow2\left(x+y+z\right)=4\Rightarrow x+y+z=2\)
*)Xét \(x+y=12\Rightarrow x+y+z=z+12\)
\(\Rightarrow2=z+12\Rightarrow z=-10\)
*)Xét \(y+z=-16\Rightarrow x+y+z=-16+x\)
\(\Rightarrow2=-16+x\Rightarrow x=18\)
*)Xét \(x+z=8\Rightarrow x+y+z=8+y\)
\(\Rightarrow2=8+y\Rightarrow y=6\)