The solution of the system is: [tex]x=-3[/tex] and [tex]y=4[/tex]
Explanation
Given linear system is ......
[tex]2x+3y=6\\ \\ -8x-3y=12[/tex]
So, the co efficient matrix, [tex]A=\left[\begin{array}{cc}2&3\\-8&-3\end{array}\right][/tex]
and the answer-column matrix : [tex]\left[\begin{array}{c}6\\12\end{array}\right][/tex]
Now, we will replace the x and y column in the co efficient matrix by the answer-column matrix for getting [tex]A_{x}[/tex] and [tex]A_{y}[/tex] respectively.
So, [tex]A_{x}= \left[\begin{array}{cc}6&3\\12&-3\end{array}\right][/tex] and [tex]A_{y}= \left[\begin{array}{cc}2&6\\-8&12\end{array}\right][/tex]
Now, we will find determinant of each matrix. So.....
[tex]|A| = -6-(-24)= -6+24=18\\ \\ |A_{x}| =-18-36=-54\\ \\ |A_{y}|=24-(-48)=24+48=72[/tex]
According to the Cramer's rule, [tex]x= \frac{|A_{x}|}{|A|}[/tex] and [tex]y= \frac{|A_{y}|}{|A|}[/tex]
So....
[tex]x= \frac{-54}{18}=-3\\ \\ y= \frac{72}{18}=4[/tex]
