Answer:
Option D) is correct
That is x=2 , y=-5
Step-by-step explanation:
Given that the [tex]|A|=\left| \begin{array}{cc}4&-6\\ 8&-2\end{array}\right|, \left|A_x\right|=\left|\begin{array}{cc}38&-6\\ 28&-2\end{array}\right|, \left|A_y\right|=\left|\begin{array}{cc}4&38\\ 8&26\end{array}\right|[/tex]
To find their determinants
[tex]|A|=\left| \begin{array}{cc}4&-6\\ 8&-2\end{array}\right|[/tex]
=-8+48
=40
Therefore [tex]|A|=40[/tex]
[tex]|A_x|=\left|\begin{array}{cc}38&-6\\ 28&-2\end{array}\right|[/tex]
=-76+156
=80
Therefore [tex]|A_x|=80[/tex]
[tex]|A_y|=\left|\begin{array}{cc}4&38\\ 8&26\end{array}\right|[/tex]
=104-304
=-200
Therefore [tex]|A_y|=-200[/tex]
To find the values of x and y:
[tex]x=\frac{|A_x|}{|A|}\ \textrm{and}\ y=\frac{|A_y|}{|A|}[/tex]
[tex]x=\frac{80}{40}[/tex] and [tex]y=\frac{-200}{40}[/tex]
x=2 and y=-5
Option D) is correct
That is x=2 , y=-5
