Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 3 Linear Systems and Matrices - 3.8 Use Inverse Matrices to Solve Linear Systems - 3.8 Exercises - Quiz for Lessons 3.6-3.8 - Page 217: 13

Answer

$x=-2, y=6$

Work Step by Step

Rewrite our system of equations in matrix form: $\begin{bmatrix} 4 & 1\\ -6 &1 \end{bmatrix}.\begin{bmatrix} x\\ y \end{bmatrix}=\begin{bmatrix} -2\\ 18 \end{bmatrix}$ $\begin{bmatrix} x\\ y \end{bmatrix}=\frac{1}{4+6}\begin{bmatrix} 1&-1\\ 6 &4 \end{bmatrix}.\begin{bmatrix} -2\\ 18 \end{bmatrix}$ $\begin{bmatrix} x\\ y \end{bmatrix}=\frac{1}{10}\begin{bmatrix} -20\\ 60 \end{bmatrix}$ $\begin{bmatrix} x\\ y \end{bmatrix}=\begin{bmatrix} -2\\ 6 \end{bmatrix}$ Hence, $x=-2, y=6$
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