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Question Number 168361 by leicianocosta last updated on 08/Apr/22

Answered by som(math1967) last updated on 09/Apr/22

$$\mathit{x}=-\mathit{k}\mathit{z}-5$$$$\mathit{x}+5=-\mathit{k}\mathit{z}$$$$\frac{\mathit{x}+5}{-\mathit{k}}=\mathit{z}$$$$\mathit{y}=-3\mathit{z}\Rightarrow \frac{y}{-3}=\mathit{z}$$$$\mathit{e}\mathit{q}\mathit{u}\mathit{n}.\mathit{o}\mathit{f}\mathit{r}\frac{\mathit{x}+5}{-\mathit{k}}=\frac{\mathit{y}}{-3}=\frac{\mathit{z}}{1}$$$$equn.of\mathit{s}$$$$\frac{\mathit{x}+3}{-1}=\frac{\mathit{y}-2}{-2}=\frac{\mathit{z}+1}{1}$$$$\mathit{r}\mathit{a}\mathit{n}\mathit{d}\mathit{s}\mathit{p}\mathit{e}\mathit{r}\mathit{p}\mathit{e}\mathit{n}\mathit{d}\mathit{i}\mathit{c}\mathit{u}\mathit{l}\mathit{a}\mathit{r}$$$$(-\mathit{k})(-1)+(-3)(-2)+\left(1\right)\left(1\right)=0$$$$\Rightarrow \mathit{k}+7=0\therefore \mathit{k}=-7$$

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