Question

30 POINTS! Consider the system of linear equations and the matrix equations below.

What is the value of x in the equation?

Answer 1

7

Explanation:

right on edge

Answer 2

Option C is correct.

Explanation:

-x+3y=2

4x-2y=22

In matrix form is represented as:

`\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]`

AX=B

`X = A^(-1)B`

`A^(-1) = |A|/Adj A`

|A| = (-1)(-2)-(3)(4)

|A| = 2-12

|A| = -10

Adj A =
`\left[\begin{array}{cc}-2&-3\\-4&-1\end{array}\right]`

A^-1 = -1/10
`\left[\begin{array}{cc}-2&-3\\-4&-1\end{array}\right]`

A^-1 = 1/10
`\left[\begin{array}{cc}2&3\\4&1\end{array}\right]`

X= A^-1 B

X = 1/10
`\left[\begin{array}{cc}2&3\\4&1\end{array}\right]`
`\left[\begin{array}{c}2&22\end{array}\right]`

X=1/10
`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]`

So, x = 7 and y =3

Hence Option C is correct.