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 $\{(-7,5)\}$.