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 - Chapter Test - Page 796: 19

Answer

$\{(-2,-5)\}$

Work Step by Step

We are given the system of equations: $\begin{cases} 4x+3y=-23\\ 3x-5y=19 \end{cases}$ Compute $D,D_x,D_y,D_z$: $D=\begin{vmatrix}4&3\\3&-5\end{vmatrix}=4(-5)-3(3)=-29$ $D_x=\begin{vmatrix}-23&3\\19&-5\end{vmatrix}=-23(-5)-3(19)=58$ $D_y=\begin{vmatrix}4&-23\\3&19\end{vmatrix}=4(19)-3(-23)=145$ Determine $x$: $x=\dfrac{D_x}{D}=\dfrac{58}{-29}=-2$ Determine $y$: $y=\dfrac{D_y}{D}=\dfrac{145}{-29}=-5$ The solution set is: $\{(-2,-5)\}$
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