Answer:
[tex]X=\left[\begin{array}{cc}-\frac{97}{145}&-\frac{54}{145}\\\\\frac{20}{29}&\frac{21}{29}\end{array}\right]\\[/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{cc}9&9\\-9&-9\end{array}\right] X+\left[\begin{array}{cc}6&3\\7&9\end{array}\right] =\left[\begin{array}{cc}-1&8\\-4&6\end{array}\right] X[/tex]
[tex]Assume\:\:\:X=\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]
[tex]9a+9c+6=-a+8c\\-9a-9c+7=-4a+6c\\9b+9d+3=-b+8d\\-9b-9d+9=-4b+6d[/tex]
[tex]10a+c=-6\\5a+15c=7[/tex]
[tex]a=-\frac{97}{145} ,\:\:c=\frac{20}{29}[/tex]
[tex]10b+d=-3\\5b+15d=9[/tex]
[tex]b=-\frac{54}{145} ,\:\:d=\frac{21}{29}[/tex]
Hence,
[tex]X=\left[\begin{array}{cc}-\frac{97}{145}&-\frac{54}{145}\\\\\frac{20}{29}&\frac{21}{29}\end{array}\right]\\[/tex]
