College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 6 - Matrices and Determinants - Exercise Set 6.5 - Page 652: 13

Answer

Solution set = $\{(2,-3)\}$

Work Step by Step

$D= $determinant of the coefficient matrix $=\left|\begin{array}{ll} 12 & 3\\ 2 & -3 \end{array}\right|=-36-6=-42$ $D_{x}=$ in D, replace the x column with the constants column $= \left|\begin{array}{ll} 15 & 3\\ 13 & -3 \end{array}\right|=-45-39=-84$ $D_{y}=$ in D, replace the x column with the constants column $=\left|\begin{array}{ll} 12 & 15\\ 2 & 13 \end{array}\right|=156-30=126$ $x=\displaystyle \frac{D_{x}}{D}=\frac{-84}{-42}=2$ $y=\displaystyle \frac{D_{y}}{D}=\frac{126}{-42}=-3$ Solution set = $\{(2,-3)\}$
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