Answer
Solution set: $\{ ( 1$ , $2$ , $-1 ) \}$
Work Step by Step
Augmented matrix:
$\left[\begin{array}{lllll}
2 & 2 & 7 & | & -1\\
2 & 1 & 2 & | & 2\\
4 & 6 & 1 & | & 15
\end{array}\right]\left\{\begin{array}{l}
.\\
\leftarrow R_{2}-R_{1}\\
\leftarrow R_{3}-2R_{1}.
\end{array}\right.$
$\left[\begin{array}{lllll}
2 & 2 & 7 & | & -1\\
0 & -1 & -5 & | & 3\\
0 & 2 & -13 & | & 17
\end{array}\right]\left\{\begin{array}{l}
.\\
\times(-1)\\
\leftarrow R_{3}+2R_{2}.
\end{array}\right.$
$\left[\begin{array}{lllll}
2 & 2 & 7 & | & -1\\
0 & 1 & 5 & | & -3\\
0 & 0 & -23 & | & 23
\end{array}\right]\left\{\begin{array}{l}
.\\
.\\
\Rightarrow z=-1.
\end{array}\right.$
Back substitute into row/equation 2,
$y+5(-1)=-3$
$y=-3+5=2$
Back substitute into row/equation 1:
$2x+2(2)+7(-1)=-1$
$2x=-1+3$
$2x=2$
$x=1$
Solution set: $\{ ( 1$ , $2$ , $-1 ) \}$
