Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 10 - Systems of Equations and Inequalities - Section 10.4 Matrix Algebra - 10.4 Assess Your Understanding - Page 777: 44


$x=9, y=23 \text{ or } (9,23)$

Work Step by Step

We will write the system $\left\{\begin{array}{r}{3x-y=4}\\{-2x+y=5}\end{array}\right.$ in matrix form as: $AX=B$ where, $X=\left[\begin{array}{l}x\\y \end{array}\right]$ We have: $A=\left[\begin{array}{ll}{3}&{-1}\\{-2}&{1}\end{array}\right]$, and its inverse is: $A^{-1}=\left[\begin{array}{rr}{1}&{1}\\{2}&{3}\end{array}\right]$ Thus, the solution of the given matrix can be expressed as: $X=A^{-1}B=\left[\begin{array}{rr}{1}&{1}\\{2}&{3}\end{array}\right]\left[\begin{array}{l} 4\\5\end{array}\right]$ $\left[\begin{array}{l} x\\y \end{array}\right]=\left[\begin{array}{l} 4+5\\ 8+15 \end{array}\right]=\left[\begin{array}{l} 9\\23\end{array}\right]$ So, our solution is: $(x, y)=(9,23)$
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