Answer
No solution
Work Step by Step
We have to solve the system:
$$\begin{align*}
\begin{cases}
x+y-z&=2\quad\quad&&\text{Equation }1\\
2x+2y-2z&=6\quad\quad&&\text{Equation }2\\
5x+y-3z&=8\quad\quad&&\text{Equation }3.
\end{cases}
\end{align*}$$
We multiply equation $1$ by $-2$ and add it to equation $2$:
$$\begin{align*}
-2x-2y+2z&=-4\quad\quad&&\text{Add }-2\text{ times equation }1\\
2x+2y-2z&=6\quad\quad&&\text{ }\\
\text{___________}&\text{______}\\
0&=2\quad\quad&&\text{New Equation }1.
\end{align*}$$
As we obtain a false equation, we conclude that the original system has no solution.
