30 POINTS! Consider the system of linear equations and the matrix equations below.What is the value of x in the equation?
Accepted Solution
A:
Answer:Option C is correct.Step-by-step explanation:-x+3y=24x-2y=22In matrix form is represented as:[tex]\left[\begin{array}{cc}-1&3\\4&-2\end{array}\right] \left[\begin{array}{c}x&y\end{array}\right] =\left[\begin{array}{c}2&22\end{array}\right][/tex]AX=B[tex]X = A^{-1}B[/tex][tex]A^{-1} = |A|/Adj A[/tex]|A| = (-1)(-2)-(3)(4)|A| = 2-12|A| = -10Adj A = [tex]\left[\begin{array}{cc}-2&-3\\-4&-1\end{array}\right][/tex]A^-1 = -1/10[tex]\left[\begin{array}{cc}-2&-3\\-4&-1\end{array}\right][/tex]A^-1 = 1/10[tex]\left[\begin{array}{cc}2&3\\4&1\end{array}\right][/tex]X= A^-1 BX = 1/10[tex]\left[\begin{array}{cc}2&3\\4&1\end{array}\right][/tex][tex]\left[\begin{array}{c}2&22\end{array}\right][/tex]X=1/10[tex]X=1/10\left[\begin{array}{c}2*2+3*22\\4*2+1*22\end{array}\right]\\X=1/10\left[\begin{array}{c}4+66\\8+22\end{array}\right]\\X=1/10\left[\begin{array}{c}70\\30\end{array}\right]\\X=\left[\begin{array}{c}70/10\\30/10\end{array}\right]\\X=\left[\begin{array}{c}7\\3\end{array}\right][/tex]So, x = 7 and y =3Hence Option C is correct.