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: 45


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

Work Step by Step

We are given the system of equations: $\begin{cases} 2x+3y=6\\ x-y=\frac{1}{2} \end{cases}$ Write the augmented matrix: $\begin{bmatrix}2&3&|&6\\1&-1&|&\frac{1}{2}\end{bmatrix}$ Perform row operations to bring the matrix to the reduced row echelon form: $R_1=-r_2+r_1$ $\begin{bmatrix}1&4&|&\frac{11}{2}\\1&-1&|&\frac{1}{2}\end{bmatrix}$ $R_2=-r_1+r_2$ $\begin{bmatrix}1&4&|&\frac{11}{2}\\0&-5&|&-5\end{bmatrix}$ $R_2=-\dfrac{1}{5}r_2$ $\begin{bmatrix}1&4&|&\frac{11}{2}\\0&1&|&1\end{bmatrix}$ $R_1=-4r_2+r_1$ $\begin{bmatrix}1&0&|&\frac{3}{2}\\0&1&|&1\end{bmatrix}$ Write the corresponding system of equations: $\begin{cases} 1x+0y=\frac{3}{2}\\ 0x+1y=1 \end{cases}$ $\begin{cases} x=\frac{3}{2}\\ y=1 \end{cases}$ The system is consistent. The solution set is: $\left\{\left(\dfrac{3}{2},1\right)\right\}$
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