Answer:
Option b is correct (8,13).
Step-by-step explanation:
7x - 4y = 4
10x - 6y =2
it can be represented in matrix form as[tex]\left[\begin{array}{cc}7&-4\\10&-6\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}4\\2\end{array}\right][/tex]
A= [tex]\left[\begin{array}{cc}7&-4\\10&-6\end{array}\right] [/tex]
X= [tex]\left[\begin{array}{c}x\\y\end{array}\right][/tex]
B= [tex] \left[\begin{array}{c}4\\2\end{array}\right][/tex]
i.e, AX=B
or X= A⁻¹ B
A⁻¹ = 1/|A| * Adj A
determinant of A = |A|= (7*-6) - (-4*10)
= (-42)-(-40)
= (-42) + 40 = -2
so, |A| = -2
Adj A= [tex]\left[\begin{array}{cc}-6&4\\-10&7\end{array}\right] [/tex]
A⁻¹ = [tex]\left[\begin{array}{cc}-6&4\\-10&7\end{array}\right] [/tex]/ -2
A⁻¹ = [tex]\left[\begin{array}{cc}3&-2\\5&-7/2\end{array}\right] [/tex]
X= A⁻¹ B
X= [tex]\left[\begin{array}{cc}3&-2\\5&-7/2\end{array}\right] *\left[\begin{array}{c}4\\2\end{array}\right][/tex]
X= [tex]\left[\begin{array}{c}(3*4) + (-2*2)\\(5*4) + (-7/2*2)\end{array}\right][/tex]
X= [tex]\left[\begin{array}{c}12-4\\20-7\end{array}\right][/tex]
X= [tex]\left[\begin{array}{c}8\\13\end{array}\right][/tex]
x= 8, y= 13
solution set= (8,13).
Option b is correct.
