Chapter 10 - 10.3 - The Inverse of a Square Matrix - 10.3 Exercises - Page 735: 41

$x= -8; y=-6$

Work Step by Step

The system can be written as: $AX=B$ where, $X= \begin{bmatrix} x \\ y \end{bmatrix}$ When there is an inverse of a matrix $A A^{-1} = I$ (the Identity Matrix) Thus, $X=A^{-1} B = \begin{bmatrix} -3 &2 \\ -2 & 1 \end{bmatrix} \begin{bmatrix} 4 \\ 2 \end{bmatrix} = \begin{bmatrix} (-3) (4)+(2)(2) \\ (-2) (4) +(1)(2) \end{bmatrix}=\begin{bmatrix} -8 \\ -6 \end{bmatrix}$ So, $X= \begin{bmatrix} x \\ y \end{bmatrix}=\begin{bmatrix} -8 \\ -6 \end{bmatrix}$ Therefore, $x= -8; y=-6$

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