$\left\{\begin{matrix}\\x=-\left(y+z\right)\text{, }&\text{unconditionally}\\x=z\text{, }&y=z\end{matrix}\right.$

$\left\{\begin{matrix}\\y=-\left(x+z\right)\text{, }&\text{unconditionally}\\y=z\text{, }&x=z\end{matrix}\right.$