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: 20



Work Step by Step

We are given the system of equations: $\begin{cases} 4x-3y+2z=15\\ -2x+y-3z=-15\\ 5x-5y+2z=18 \end{cases}$ Compute $D,D_x,D_y,D_z$: $D=\begin{vmatrix}4&-3&2\\-2&1&-3\\5&-5&2\end{vmatrix}=4(-13)-(-3)(11)+2(5)=-9$ $D_x=\begin{vmatrix}15&-3&2\\-15&1&-3\\18&-5&2\end{vmatrix}=15(-13)-(-3)(24)+2(57)=-9$ $D_y=\begin{vmatrix}4&15&2\\-2&-15&-3\\5&18&2\end{vmatrix}=4(24)-15(11)+2(39)=9$ $D_z=\begin{vmatrix}4&-3&15\\-2&1&-15\\5&-5&18\end{vmatrix}=4(-57)-(-3)(39)+15(5)=-36$ Determine $x$: $x=\dfrac{D_x}{D}=\dfrac{-9}{-9}=1$ Determine $y$: $y=\dfrac{D_y}{D}=\dfrac{9}{-9}=-1$ Determine $z$: $z=\dfrac{D_z}{D}=\dfrac{-36}{-9}=4$ The solution set is: $\{(1,-1,4)\}$
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