Solve the system by using a matrix equation

Answer:Option A is correct (17,11).Step-by-step explanation:6x - 9y = 33x - 4y =7it can be represented in matrix form as[tex]\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}3\\7\end{array}\right][/tex]A= [tex]\left[\begin{array}{cc}6&-9\\3&4\end{array}\right] [/tex] X= [tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex]B= [tex] \left[\begin{array}{c}3\\7\end{array}\right][/tex]i.e, AX=Bor X= A⁻¹ BA⁻¹ = 1/|A| * Adj Adeterminant of A = |A|= (6*-4) - (-9*3)                                     = (-24)-(-27)                                     = (-24) + 27 = 3so, |A| = 3Adj A=  [tex]\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right] [/tex] A⁻¹ =  [tex]\left[\begin{array}{cc}-4&9\\-3&6\end{array}\right] [/tex]/3A⁻¹ =  [tex]\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] [/tex]X= A⁻¹ BX=  [tex]\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] *\left[\begin{array}{c}3\\7\end{array}\right][/tex]X= [tex]\left[\begin{array}{c}(-4/3*3) + (3*7)\\(-1*3) + (2*7)\end{array}\right][/tex]X= [tex]\left[\begin{array}{c}-4+21\\-3+14\end{array}\right][/tex]X= [tex]\left[\begin{array}{c}17\\11\end{array}\right][/tex]x= 17, y= 11solution set= (17,11).