Answer
$(x,y,z)=(19,7,5)$.
Work Step by Step
The augmented matrix is
$\begin{bmatrix}
1&0 &-3 & 4\\
0 & 1 & -1 & 2\\
0& 0 & 1 & 5
\end{bmatrix}$.
For the linear equation.
First column $=$ coefficients of $x$.
Second column $=$ coefficients of $y$
Third column $=$ coefficients of $z$
and fourth column $=$ the right-hand side.
The given matrix is a upper triangular form.
Rewrite the third row as a linear equation.
$\Rightarrow 0x+0y+1z=5$
$\Rightarrow z=5$
Rewrite the second row as a linear equation.
$\Rightarrow 0x+1y-1z=2$
$\Rightarrow y-z=2$
Substitute $z=5$.
$\Rightarrow y-(5)=2$
Clear the parentheses.
$\Rightarrow y-5=2$
Add $3$ to both sides.
$\Rightarrow y-5+5=2+5$
Simplify.
$\Rightarrow y=7$
Rewrite the first row as a linear equation.
$\Rightarrow 1x+0y-3z=4$
$\Rightarrow x-3z=4$
Substitute $z=5$.
$\Rightarrow x-3(5)=4$
Clear the parentheses.
$\Rightarrow x-15=4$
Add $15$ to both sides.
$\Rightarrow x-15+15=4+15$
Simplify.
$\Rightarrow x=19$
The solution set is $(x,y,z)=(19,7,5)$.
