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Question Number 1771 by hareem ali last updated on 19/Sep/15

$$2x-y+2z=4$$$$x+10y-3z=10$$

Answered by 123456 last updated on 19/Sep/15

$$\left[\begin{array}{ccc}2& -1& 2\\ 1& 10& -3\\ 0& 0& 0\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}4\\ 10\\ 0\end{array}\right]$$$$\left[\begin{array}{cccc}2& -1& 2& 4\\ 1& 10& -3& 10\end{array}\right]$$$$\sim \left[\begin{array}{cccc}2& -1& 2& 4\\ 2& 20& -6& 20\end{array}\right]$$$$\sim \left[\begin{array}{cccc}2& -1& 2& 4\\ 0& 21& -8& 16\end{array}\right]$$$$\sim \left[\begin{array}{cccc}42& -21& 42& 84\\ 0& 21& -8& 16\end{array}\right]$$$$\sim \left[\begin{array}{cccc}42& 0& 34& 100\\ 0& 21& -8& 16\end{array}\right]$$$$\sim \left[\begin{array}{cccc}1& 0& \frac{17}{21}& \frac{50}{21}\\ 0& 1& -\frac{8}{21}& \frac{16}{21}\end{array}\right]$$$$\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}\frac{50-17t}{21}\\ \frac{16+8t}{21}\\ t\end{array}\right]$$

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