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 - 11.2 Systems of Linear Equations: Matrices - 11.2 Assess Your Understanding - Page 731: 47


Consistent Solution set: $\left\{\left(\dfrac{4}{3},\dfrac{1}{5}\right)\right\}$

Work Step by Step

We are given the system of equations: $\begin{cases} 3x-5y=3\\ 15x+5y=21 \end{cases}$ Write the augmented matrix: $\begin{bmatrix} 3&-5&|&3\\15&5&|&21\end{bmatrix}$ Perform row operations to bring the matrix to the reduced row echelon form: $R_2=-5r_1+r_2$ $\begin{bmatrix} 3&-5&|&3\\0&30&|&6\end{bmatrix}$ $R_1=\dfrac{1}{3}r_1$ $\begin{bmatrix}1&-\frac{5}{3}&|&1\\0&30&|&6\end{bmatrix}$ $R_2=\dfrac{1}{30}r_2$ $\begin{bmatrix}1&-\frac{5}{3}&|&1\\0&1&|&\frac{1}{5}\end{bmatrix}$ $R_1=\dfrac{5}{3}r_2+r_1$ $\begin{bmatrix}1&0&|&\frac{4}{3}\\0&1&|&\frac{1}{5}\end{bmatrix}$ Write the corresponding system of equations: $\begin{cases} 1x+0y=\frac{4}{3}\\ 0x+1y=\frac{1}{5} \end{cases}$ $\begin{cases} x=\frac{4}{3}\\ y=\frac{1}{5} \end{cases}$ The system is consistent. The solution set is: $\left\{\left(\dfrac{4}{3},\dfrac{1}{5}\right)\right\}$
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