Answer
$(\displaystyle \frac{21}{2},\frac{13}{2})$
Work Step by Step
Write the augmented matrix and,
using row transformations arrive at the reduced row echelon form.
-----------
Swap equations 1 and 2,
remove decimals/fractions
$\left[\begin{array}{lll}
1 & - 1 & 4\\
-0.3 & 0.5 & 0.1\\
1/17 & 1/17 & 1
\end{array}\right]\begin{array}{l}
.\\
\times 10.\\
\times 17.
\end{array}$
$\left[\begin{array}{lll}
1 & - 1 & 4\\
- 3 & 5 & 1\\
1 & 1 & 17
\end{array}\right]\begin{array}{l}
.\\
R_{2}+3R_{1}.\\
R_{3}-R_{1} .
\end{array}$
... clears column $1,$
$\left[\begin{array}{lll}
1 & - 1 & 4\\
0 & 2 & 13\\
0 & 2 & 13
\end{array}\right]\begin{array}{l}
R_{1}+\frac{1}{2}R_{2}.\\
\times\frac{1}{2} .\\
R_{3}-R_{2} .
\end{array}$
... leading 1 in row 2,
... clear column $2,$
$\rightarrow\left[\begin{array}{lll}
1 & 0 & 21/2\\
0 & 1 & 13/2\\
0 & 0 & 0
\end{array}\right]$
Last row: all zeros, so system is consistent.
Solution: $(\displaystyle \frac{21}{2},\frac{13}{2})$
