Answer
The system represented by the augmented matrix is
$\left\{\begin{array}{lll}
x & -3y & =-2\\
2x & -5y & =5
\end{array}\right.$
Performing the row operation,
$\rightarrow\left[\begin{array}{cc|c}
{1}&{-3}&{-2}\\
{0}&{1}&{9}\end{array}\right]$
Work Step by Step
The system represented by the augmented matrix is
$\left\{\begin{array}{lll}
x & -3y & =-2\\
2x & -5y & =5
\end{array}\right.$
Performing the row operation,
$\left[\begin{array}{rr|r}
{1}&{-3}&{-2}\\
{2}&{-5}&{5}\end{array}\right]\rightarrow R_{2}=-2r_{1}+r_{2}\rightarrow$
$\rightarrow\left[\begin{array}{cc|c}
{1}&{-3}&{-2}\\
{-2(1)+2}&{2(-3)-5}&{-2(-2)+5}\end{array}\right]\rightarrow\left[\begin{array}{cc|c}
{1}&{-3}&{-2}\\
{0}&{1}&{9}\end{array}\right]$
