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Question Number 46785 by Tawa1 last updated on 31/Oct/18

$$\mathrm{Solve}\mathrm{the}\mathrm{system}:$$$$\mathrm{x}+\mathrm{y}+\mathrm{z}=30.....\mathrm{equation}\left(\mathrm{i}\right)$$$$\frac{\mathrm{x}}{3}+\frac{\mathrm{y}}{2}+2\mathrm{z}=30......\mathrm{equation}\left(\mathrm{ii}\right)$$$$$$

Answered by MJS last updated on 31/Oct/18

$$\mathrm{these}\mathrm{are}2\mathrm{planes}\mathrm{in}{\mathbb{R}}^3\Rightarrow \mathrm{we}\mathrm{get}\mathrm{a}\mathrm{line}$$$$\left(1\right)\Rightarrow z=-x-y+30$$$$\left(2\right)\Rightarrow z=-\frac{1}{6}x-\frac{1}{4}y+15$$$$-x-y+30=-\frac{1}{6}x-\frac{1}{4}y+15$$$$y=-\frac{10}{9}x+20\Rightarrow z=\frac{1}{9}x+10$$$$\mathrm{put}x=9t$$$$l:\left(\begin{array}{c}x\\ y\\ z\end{array}\right)=\left(\begin{array}{c}0\\ 20\\ 10\end{array}\right)+t\times \left(\begin{array}{c}9\\ -10\\ 1\end{array}\right)$$

Commented by Tawa1 last updated on 31/Oct/18

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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