Answer:
Option A is correct (17,11).
Step-by-step explanation:
6x - 9y = 3
3x - 4y =7
it 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=B
or X= A⁻¹ B
A⁻¹ = 1/|A| * Adj A
determinant of A = |A|= (6*-4) - (-9*3)
= (-24)-(-27)
= (-24) + 27 = 3
so, |A| = 3
Adj 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]/3
A⁻¹ = [tex]\left[\begin{array}{cc}-4/3&3\\-1&2\end{array}\right] [/tex]
X= A⁻¹ B
X= [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= 11
solution set= (17,11).
