## Precalculus (10th Edition)

$\{(2,-1)\}$
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: $\{(2,-1)\}$