College Algebra (11th Edition)

Published by Pearson
ISBN 10: 0321671791
ISBN 13: 978-0-32167-179-0

Chapter 5 - Section 5.1 - Systems of Linear Equations - 5.1 Exercises - Page 486: 25

Answer

The solution set is $\{(2,-2)\}$

Work Step by Step

Write each equation in standard form to obtain: \begin{align*} 6x+7y=-2 ~~~&(1) \\ 7x-6y=26 ~~~&(2)\end{align*} Multiply the first equation by $6$ and second equation by $7$ to obtain the equivalent system: \begin{align*}36x+42y=-12 ~~~&(3) \\ 49x-42y=182 ~~~&(4)\end{align*} Add equations $(3)$ and $(4)$ to eliminate $y$ and then solve for $x$. \begin{align*}36x+42y+49x-42y&=-12+182 \\ 85x&=170 \\ x&=2\end{align*} Plug $x=2$ into the first equation then solve for $y$ to obtain: \begin{align*}(6)(2)+7y&=-2 \\ 12+7y&=-2\\ y&=-2\end{align*} Thus, the solution set is $\{(2,-2)\}$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.