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: 21

Answer

The solution set is $\{(1, 3)\}$.

Work Step by Step

We are given the system of equations as: $2x-3y=-7 ~~~(1) \\ -5x-4y=-17 ~~~(2)$ By multiplying equation $(1)$ by $5$ and equation $(2)$ by $2$, then first and second equation are equivalent to: $10x-15y=-35 ~~~(3) \\ -10x-8y=-34 ~~~(4)$ Add equations $(3)$ and $(4)$ to eliminate $x$ and then solve for $y$. \begin{align*} 10x-15y+(-10x-8y)&=-35 +(-34) \\ 10x-15y-10x-8y&=-69 \\ -23 y&=-69 \\ y&=3 \end{align*} Plug $y=3$ into the first equation then solve for $x$ to obtain: \begin{align*} 2x-(3)(3)=-7 \\ 2x-9=-7 \\x=1 \end{align*} So, the solution set is $\{(1, 3)\}$.
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.