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: 24

Answer

The solution set is $\{(2,3)\}$.

Work Step by Step

Multiply the second equation by $-4$ to obtain the equivalent system: \begin{align*}12x-5y&=9 \quad \quad\quad&(1)\\ -12x+32y&=72 \quad \quad&(2)\end{align*} Add equations $(1)$ and $(2)$ to eliminate $x$ and then solve for $y$. \begin{align*} 12x-5y+(-12x+32y)&=9+72 \\ 27y&=81 \\ y&=3 \end{align*} Plug $y=3$ into the first equation then solve for $x$ to obtain: \begin{align*} 12x-(5)(3)&=9 \\ 12x-15&=9 \\x&=2 \end{align*} Thus, the solution set is $\{(2,3)\}$.
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