Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 8 - Section 8.5 - Determinants and Cramer's Rule - Exercise Set - Page 945: 14



Work Step by Step

As per Cramer's Rule , we have $x=\dfrac{D_x}{D}$ and $y=\dfrac{D_y}{D}$ The general formula to calculate the determinant of a $2 \times 2$ matrix which has 2 rows and 2 columns, such as: $D=\begin{vmatrix}a&b\\c&d\end{vmatrix}=ad-bc$ Thus, $D=\begin{vmatrix}1&-2\\5&-1\end{vmatrix}=9$ and $D_x=\begin{vmatrix}5&-2\\-2&-1\end{vmatrix}=-9$ Also, $D_y=\begin{vmatrix}1&5\\5&-2\end{vmatrix}=-27$ Now, $x=\dfrac{D_x}{D}=-1$ and $y=\dfrac{D_y}{D}=-3$ Hence, $(x,y)=(-1,-3)$
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