Question

Solve the system by using the inverse of the coefficient matrix. -3x + 9y = 9 3x + 2y = 13 Group of answer choices

Answer 1

Answer:

x= 3

y=2

Step-by-step explanation:

-3x + 9y = 9 ----------- equation 1

3x + 2y = 13--------------- equation 2

In  Matrix Form                            

$\left[\begin{array}{cc}-3&9\\3&2\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}9\\13\end{array}\right]$                  

Let A = $\left[\begin{array}{cc}-3&9\\3&2\end{array}\right]$    X =  $\left[\begin{array}{c}x\\y\end{array}\right]$  and B =    $\left[\begin{array}{c}9\\13\end{array}\right]$  

Then Mathematically AX= B

or X= A⁻¹ B

Where A⁻¹ = Adjacent A/ mod of A

Adjacent A =   $\left[\begin{array}{cc}2&-9\\-3&-3\end{array}\right]$    

Mod Of A= -6 - (27) = -33 which is not equal to zero

so Putting These values in the given formula

X= 1/-33    $\left[\begin{array}{cc}2&-9\\-3&-3\end{array}\right]$      $\left[\begin{array}{c}9\\13\end{array}\right]$  

Now Multiplying Rows and Columns

   $\left[\begin{array}{c}x\\y\end{array}\right]$ = -1/33    $\left[\begin{array}{cc}2*9+- 9*13\\-3*9 +- 3*13\end{array}\right]$

Solving the Matrix we get

  $\left[\begin{array}{c}x\\y\end{array}\right]$ = -1/33  $\left[\begin{array}{cc}18-117\\-27-39\\\end{array}\right]$

  $\left[\begin{array}{c}x\\y\end{array}\right]$ = -1/33  $\left[\begin{array}{cc}-99\\-66\end{array}\right]$

From Here we find x= 99/33 or 3

and y = 66/33= 2