Solve for x
\left\{\begin{matrix}\\x=0\text{, }&\text{unconditionally}\\x\in \mathrm{R}\text{, }&\left(y=-\frac{5}{z}\text{ and }z\neq 0\right)\text{ or }y=0\end{matrix}\right.
Solve for y
\left\{\begin{matrix}\\y=0\text{, }&\text{unconditionally}\\y=-\frac{5}{z}\text{, }&z\neq 0\\y\in \mathrm{R}\text{, }&x=0\end{matrix}\right.
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-5xy-zxy^{2}=0
Subtract zxy^{2} from both sides.
-5xy-xzy^{2}=0
Reorder the terms.
\left(-5y-zy^{2}\right)x=0
Combine all terms containing x.
x=0
Divide 0 by -5y-zy^{2}.
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