Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 11 - Systems of Equations and Inequalities - Chapter Review - Review Exercises - Page 794: 29



Work Step by Step

We are given the system of equations: $\begin{cases} x-2y=4\\ 3x+2y=4 \end{cases}$ Compute $D,D_x,D_y$: $D=\begin{vmatrix}1&-2\\3&2\end{vmatrix}=1(2)-3(-2)=8$ $D_x=\begin{vmatrix}4&-2\\4&2\end{vmatrix}=4(2)-4(-2)=16$ $D_y=\begin{vmatrix}1&4\\3&4\end{vmatrix}=1(4)-3(4)=-8$ Determine $x$: $x=\dfrac{D_x}{D}=\dfrac{16}{8}=2$ Determine $y$: $y=\dfrac{D_y}{D}=\dfrac{-8}{8}=-1$ The solution set is: $\{(2,-1)\}$
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