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 - Chapter Review - Review Exercises - Page 794: 30



Work Step by Step

We are given the system of equations: $\begin{cases} 2x+3y-13=0\\ 3x-2y=0 \end{cases}$ Bring the system to standard form: $\begin{cases} 2x+3y=13\\ 3x-2y=0 \end{cases}$ Compute $D,D_x,D_y$: $D=\begin{vmatrix}2&3\\3&-2\end{vmatrix}=2(-2)-3(3)=-13$ $D_x=\begin{vmatrix}13&3\\0&-2\end{vmatrix}=13(-2)-0(3)=-26$ $D_y=\begin{vmatrix}2&13\\3&0\end{vmatrix}=2(0)-3(13)=-39$ Determine $x$: $x=\dfrac{D_x}{D}=\dfrac{-26}{-13}=2$ Determine $y$: $y=\dfrac{D_y}{D}=\dfrac{-39}{-13}=3$ The solution set is: $\{(2,3)\}$
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