Question

Solve the equations
$x+y+z=6x-y+z=22x+y-z=1$

Answer 1

$x+y+z=1$

$6x-y+z=1$

$22x+y-z=1$

$\left[\begin{array}{ccc}1& 1& 1\\ 6& -1& 1\\ 22& 1& -1\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right]$

$\Rightarrow$ Applying $R_3\to R_3+R_2$

$\Rightarrow \left[\begin{array}{ccc}1& 1& 1\\ 6& -1& 1\\ 28& 0& 0\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\end{array}\right]=\left[\begin{array}{c}1\\ 1\\ 2\end{array}\right]$

$\Rightarrow 28x=2$

$x=\frac{1}{14}$