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: 16



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, $D=\begin{vmatrix}3&2\\2&2\end{vmatrix}=2$ and $D_x=\begin{vmatrix}2&2\\3&2\end{vmatrix}=-2$ Also, $D_y=\begin{vmatrix}3&2\\2&3\end{vmatrix}=5$ Now, $x=\dfrac{D_x}{D}=-1$ and $y=\dfrac{D_y}{D}=\dfrac{5}{2}$ Hence, $(x,y)=(-1,\dfrac{5}{2})$
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