Answer
$
X
=
\begin{bmatrix}
2 & -2
\\
-5 & 4
\end{bmatrix}$
Work Step by Step
Using the properties of matrix equality, the given matrix equation, $
3X+
\begin{bmatrix}
-2 & 1
\\
7 & -3
\end{bmatrix}
=
\begin{bmatrix}
4 & -5
\\
-8 & 9
\end{bmatrix}
,$ is equivalent to
\begin{align*}
3X+
\begin{bmatrix}
-2 & 1
\\
7 & -3
\end{bmatrix}
-
\begin{bmatrix}
-2 & 1
\\
7 & -3
\end{bmatrix}
&=
\begin{bmatrix}
4 & -5
\\
-8 & 9
\end{bmatrix}
-
\begin{bmatrix}
-2 & 1
\\
7 & -3
\end{bmatrix}
\\\\
3X
&=
\begin{bmatrix}
4-(-2) & -5-1
\\
-8-7 & 9-(-3)
\end{bmatrix}
\\\\
3X
&=
\begin{bmatrix}
4+2 & -5-1
\\
-8-7 & 9+3
\end{bmatrix}
\\\\
3X
&=
\begin{bmatrix}
6 & -6
\\
-15 & 12
\end{bmatrix}
\\\\
\left(\dfrac{1}{3}\right)3X
&=
\dfrac{1}{3}\begin{bmatrix}
6 & -6
\\
-15 & 12
\end{bmatrix}
\\\\
X
&=
\begin{bmatrix}
6\cdot\dfrac{1}{3} & -6\cdot\dfrac{1}{3}
\\
-15\cdot\dfrac{1}{3} & 12\cdot\dfrac{1}{3}
\end{bmatrix}
\\\\
X
&=
\begin{bmatrix}
2 & -2
\\
-5 & 4
\end{bmatrix}
.\end{align*}
Hence, $
X
=
\begin{bmatrix}
2 & -2
\\
-5 & 4
\end{bmatrix}.$
