Answer
$X
=
\begin{bmatrix}
2 & 5
\\
1 & 1
\end{bmatrix}$
Work Step by Step
Using the properties of matrices, the given matrix equation, $
2\begin{bmatrix}
-1 & 3
\\
-2 & 0
\end{bmatrix}
-3X
=
\begin{bmatrix}
-8 & -9
\\
-7 & -3
\end{bmatrix}
,$ is equivalent to
\begin{align*}\require{cancel}
\begin{bmatrix}
-1(2) & 3(2)
\\
-2(2) & 0(2)
\end{bmatrix}
-3X
&=
\begin{bmatrix}
-8 & -9
\\
-7 & -3
\end{bmatrix}
\\\\
\begin{bmatrix}
-2 & 6
\\
-4 & 0
\end{bmatrix}
-3X
&=
\begin{bmatrix}
-8 & -9
\\
-7 & -3
\end{bmatrix}
\\\\
-3X
&=
\begin{bmatrix}
-8 & -9
\\
-7 & -3
\end{bmatrix}
-\begin{bmatrix}
-2 & 6
\\
-4 & 0
\end{bmatrix}
\\\\
-3X
&=
\begin{bmatrix}
-8-(-2) & -9-6
\\
-7-(-4) & -3-0
\end{bmatrix}
\\\\
-3X
&=
\begin{bmatrix}
-8+2 & -9-6
\\
-7+4 & -3-0
\end{bmatrix}
\\\\
-3X
&=
\begin{bmatrix}
-6 & -15
\\
-3 & -3
\end{bmatrix}
\\\\
\left(-\dfrac{1}{3}\right)(-3X)
&=
-\dfrac{1}{3}\begin{bmatrix}
-6 & -15
\\
-3 & -3
\end{bmatrix}
\\\\
X
&=
\begin{bmatrix}
-6\left(-\dfrac{1}{3}\right) & -15\left(-\dfrac{1}{3}\right)
\\
-3\left(-\dfrac{1}{3}\right) & -3\left(-\dfrac{1}{3}\right)
\end{bmatrix}
\\\\
X
&=
\begin{bmatrix}
2 & 5
\\
1 & 1
\end{bmatrix}
.\end{align*}
Hence, the solution is $
X
=
\begin{bmatrix}
2 & 5
\\
1 & 1
\end{bmatrix}
.$
