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: 20

Answer

The solution set is $\{(-7,5)\}$.

Work Step by Step

We are given the system of equations as: $4x+y=-23 ~~~(1) \\ x-2y=-17 ~~~(2)$ By multiplying first equation by $2$ and then the first equation is equivalent to: $8x+2y=-46 ~~~(3)$ Add equations (2) and (3) to eliminate $y$ and then solve for $x$. $x-2y+8x+2y=-17-46 \\ 9x=-63 \\ x=-7$ Plug $x=-7$ into the second equation and then solve for x to obtain: $-7-2y=-17 \\ -2y= -10 \\ y=5$ So, the solution set is $\{(-7,5)\}$.
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