Answer
$\{(2,-1)\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
2x-y=5\\
5x+2y=8
\end{cases}$
Use the elimination method. Multiply the first equation by 2 and add it to the second to eliminate $y$ and find $x$:
$2(2x-y)+5x+2y=2(5)+8$
$4x-2y+5x+2y=10+8$
$9x=18$
$x=2$
Substitute $x=2$ in the first equation of the given system and determine $y$:
$2x-y=5$
$2(2)-y=5$
$4-y=5$
$y=-1$
The solution set is:
$\{(2,-1)\}$
