Answer
Solution set: $\{ ( -13t+5$ , $5t$ , $t )$ , $t\in \mathbb{R}\}$
Work Step by Step
Augmented matrix:
$\left[\begin{array}{lllll}
1 & 2 & 3 & | & 5\\
0 & 1 & -5 & | & 0
\end{array}\right]$
is already in row echelon form, so no row operations are necessary.
The system is consistent and does not have a unique solution.
Let $z=t, t\in \mathbb{R}$.
Substituting into row 2,
$y-5t=0$
$y=5t$
Substituting into row 1,
$x+2(5t)+3t=5$
$x+13t=5$
$x=-13t+5$
Solution set: $\{ ( -13t+5$ , $5t$ , $t )$ , $t\in \mathbb{R}\}$
