Answer
$(x,y)=(-34,30)$.
Work Step by Step
The given system of equations is
$-4x-4y=16$
$4x+5y=14$
The augmented matrix is
$\Rightarrow \left[\begin{array}{cc|c}
-4 & -4 & 16\\
4 & 5 & 14
\end{array}\right]$
Perform $R_1\rightarrow \frac{R_1}{-4}$.
$\Rightarrow \left[\begin{array}{cc|c}
-4/(-4) & -4/(-4) & 16/(-4)\\
4 & 5 & 14
\end{array}\right]$
Simplify.
$\Rightarrow \left[\begin{array}{cc|c}
1 & 1 & -4\\
4 & 5 & 14
\end{array}\right]$
Perform $R_2\rightarrow R_2- 4R_1$.
$\Rightarrow \left[\begin{array}{cc|c}
1 & 1 & -4\\
4-4(1) & 5-4(1) & 14-4(-4)
\end{array}\right]$
Simplify.
$\Rightarrow \left[\begin{array}{cc|c}
1 & 1 & -4\\
0 & 1 & 30
\end{array}\right]$
Perform $R_1\rightarrow R_1- R_2$.
$\Rightarrow \left[\begin{array}{cc|c}
1-0 & 1-1 & -4-30\\
0 & 1 & 30
\end{array}\right]$
Simplify.
$\Rightarrow \left[\begin{array}{cc|c}
1 & 0 & -34\\
0 & 1 & 30
\end{array}\right]$
Write each row of the matrix as an equation.
$\Rightarrow x=-34$
and
$\Rightarrow y=30$.
The solution set is $(x,y)=(-34,30)$.
