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: 15

Answer

Solution set = $\{(3,-1)\}$

Work Step by Step

$D= $determinant of the coefficient matrix $=\left|\begin{array}{ll} 4 & -5\\ 2 & 3 \end{array}\right|=4(3)-(-5)(2)=22$ $D_{x}=$ in D, replace the x column with the constants column $=\left|\begin{array}{ll} 17 & -5\\ 3 & 3 \end{array}\right|=51+15=66$ $D_{y}=$ in D, replace the x column with the constants column $=\left|\begin{array}{ll} 4 & 17\\ 2 & 3 \end{array}\right|=12-34=-22$ $x=\displaystyle \frac{D_{x}}{D}=\frac{66}{22}=3$ $y=\displaystyle \frac{D_{y}}{D}=\frac{-22}{22}=-1$ Solution set = $\{(3,-1)\}$
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