Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Appendix C - C - Exercise Set - Page 686: 29

Answer

$$x=6,y=-2,z=4$$

Work Step by Step

We solve the given system of equations using Cramer's Rule. To do this, we turn the system into two matrices. We then create x, y, and z matrices by replacing the values in the original matrix with corresponding columns in the answer matrix. We then find determinants to solve. Doing this, we find: $$ M=\begin{pmatrix}1&1&1\\ 2&-1&-1\\ 1&-2&3\end{pmatrix} \\ M_2 = \begin{pmatrix}8\\ 10\\ 22\end{pmatrix} $$ Thus: $$M_x=\begin{pmatrix}8&1&1\\ 10&-1&-1\\ 22&-2&3\end{pmatrix} \\ M_y=\begin{pmatrix}1&8&1\\ 2&10&-1\\ 1&22&3\end{pmatrix} \\ M_z=\begin{pmatrix}1&1&8\\ 2&-1&10\\ 1&-2&22\end{pmatrix} $$ So: $$x=\frac{D_x}{D}=\frac{-90}{-15} =6 \\ y=\frac{D_y}{D}=\frac{30}{-15} =-2 \\z=\frac{D_z}{D}=\frac{-60}{-15}=4 $$
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