If the solution of the system of simultaneous linear equations $x+y-z=6,3 x+2 y-z=5$ and $2 x-y-2 z+$ $3=0$ is $x=\alpha, y=\beta, z=\gamma$, then $\alpha+\beta=$

Question

Aicharya · Accepted Answer

System of equations $x+y-z=6$ $\Rightarrow 3 x+2 y-z=5 \Rightarrow 2 x-y-2 z=-3$ Augumented matrix $[A: B]=\left[\begin{array}{ccc|c}1 & 1 & -1 & 6 \ 3 & 2 & -1 & 5 \ 2 & -1 & -2 & -3\end{array}ight]$ $R_2 ightarrow R_2-3 R_1, R_3 ightarrow R_3-2 R_1$ $[\mathrm{A}: \mathrm{B}]=\left[\begin{array}{ccc|c}1 & 1 & -1 & 6 \ 0 & -1 & 2 & -13 \ 0 & -3 & 0 & -15\end{array}ight]$ $R_3 ightarrow R_3-3 R_2$ $[A: B]=\left[\begin{array}{ccc|c}1 & 1 & -1 & 6 \ 0 & -1 & 2 & -13 \ 0 & 0 & -6 & 24\end{array}ight]$ $\Rightarrow-6 z=24 \Rightarrow z=-4 \Rightarrow-y+2 z=-13 \Rightarrow y=5=\beta$ $x+y-z=6 \Rightarrow x=-3=\alpha$ $	herefore \alpha+\beta=5-3=2$

If the solution of the system of simultaneous linear equations $x+y-z=6,3 x+2 y-z=5$ and $2 x-y-2 z+$ $3=0$…

Solution