Answer
$\{(-1,2)\}$.
Work Step by Step
The given system of equations is
$2x-y=-4$
$x+3y=5$
The augmented matrix is
$\Rightarrow \left[\begin{array}{cc|c}
2 & -1& -4\\
1 & 3 &5
\end{array}\right]$
Perform $R_1\leftrightarrow R_2$.
Swap row one and row two.
$\Rightarrow \left[\begin{array}{cc|c}
1 & 3 &5 \\
2 & -1& -4
\end{array}\right]$
Perform $R_2\rightarrow R_2-2R_1$.
$\Rightarrow \left[\begin{array}{cc|c}
1 & 3 &5 \\
2-2(1) & -1-2(3)& -4-2(5)
\end{array}\right]$
Simplify.
$\Rightarrow \left[\begin{array}{cc|c}
1 & 3 &5 \\
0 & -7& -14
\end{array}\right]$
Perform $R_2\rightarrow R_2/(-7)$.
$\Rightarrow \left[\begin{array}{cc|c}
1 & 3 &5 \\
0/(-7) & -7/(-7)& -14/(-7)
\end{array}\right]$
Simplify.
$\Rightarrow \left[\begin{array}{cc|c}
1 & 3 &5 \\
0 & 1& 2
\end{array}\right]$
Perform $R_1\rightarrow R_1-3 R_2$.
$\Rightarrow \left[\begin{array}{cc|c}
1-3(0) & 3-3(1) &5-3(2) \\
0 & 1& 2
\end{array}\right]$
Simplify.
$\Rightarrow \left[\begin{array}{cc|c}
1 & 0 &-1 \\
0 & 1& 2
\end{array}\right]$
Use back substitution to solve the linear system.
$\Rightarrow x=-1$
and
$\Rightarrow y=2$.
The solution set is $\{(x,y)\}=\{(-1,2)\}$.
