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: 41


Consistent Solution set: $\left\{\left(\dfrac{1}{2},\dfrac{3}{4}\right)\right\}$

Work Step by Step

We are given the system of equations: $\begin{cases} 2x-4y=-2\\ 3x+2y=3 \end{cases}$ Write the augmented matrix: $\begin{bmatrix}2&-4&|&-2\\3&2&|&3\end{bmatrix}$ Perform row operations to bring the matrix to the reduced row echelon form: $R_1=\dfrac{1}{2}r_1$ $\begin{bmatrix}1&-2&|&-1\\3&2&|&3\end{bmatrix}$ $R_1=-3r_1+r_2$ $\begin{bmatrix}1&-2&|&-1\\0&8&|&6\end{bmatrix}$ $R_2=\dfrac{1}{8}r_2$ $\begin{bmatrix}1&-2&|&-1\\0&1&|&\frac{3}{4}\end{bmatrix}$ $R_1=2r_2+r_1$ $\begin{bmatrix}1&0&|&\frac{1}{2}\\0&1&|&\frac{3}{4}\end{bmatrix}$ Write the corresponding system of equations: $\begin{cases} x=\frac{1}{2}\\ y=\frac{3}{4} \end{cases}$ The system is consistent. Its set solution is: $\left\{\left(\dfrac{1}{2},\dfrac{3}{4}\right)\right\}$
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