Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 3 - Section 3.5 - Determinants and Cramer’s Rule - Exercise Set - Page 240: 11



Work Step by Step

General formula to calculate the determinant of matrix is: $D=\begin{vmatrix}p&q\\r&s\end{vmatrix}=ps-qr$ From question, we have $D=\begin{vmatrix}1&1\\1&-1\end{vmatrix}=(1)(-1)-(1)(1)=-2$ Now, $D_x=\begin{vmatrix}7&1\\3&-1\end{vmatrix}=(7)(-1)-(3)(1)=-10$ and $D_y=\begin{vmatrix}1&7\\1&3\end{vmatrix}=(1)(3)-(7)(3)=-4$ Apply Cramer's Rule which states that $x=\dfrac{D_x}{D}$ and $y=\dfrac{D_y}{D}$ Therefore, $x=\dfrac{D_x}{D}=\dfrac{-10}{-2}=5$ and $y=\dfrac{D_y}{D}=\dfrac{-4}{-2}=2$ Hence, our answer is: $(x,y)=(5,2)$
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