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: 19


$(x,y)=(4, 2)$

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, $D=\begin{vmatrix}3&-4\\2&2\end{vmatrix}=14$ and $D_x=\begin{vmatrix}4&-4\\12&2\end{vmatrix}=56$ Also, $D_y=\begin{vmatrix}3&4\\2&12\end{vmatrix}=28$ Now, $x=\dfrac{D_x}{D}=4$ and $y=\dfrac{D_y}{D}=2$ Hence, $(x,y)=(4, 2)$
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