Answer
The solution of the system of equations is $\left( x,y \right)=\left( 6,-1 \right)$.
Work Step by Step
We have to simplify the system of equations:
The first equation:
$\begin{align}
& \frac{x+2}{2}-\frac{y+4}{3}=3 \\
& 3x+6-2y-8=18
\end{align}$
$3x-2y=20$
And second equation:
$\begin{align}
& \frac{x+y}{5}=\frac{x-y}{2}-\frac{5}{2} \\
& 2x+2y=5x-5y-25
\end{align}$
$3x-7y=25$
And multiply equation $3x-2y=20$ by −1 to obtain:
$-3x+2y=-20$
And add equations $3x-7y=25$ and $-3x+2y=-20$ to obtain:
$\begin{align}
& 3x-7y-3x+2y=25-20 \\
& -5y=5 \\
& y=-1
\end{align}$
Put the value $y=-1$ in equation $3x-2y=20$ to obtain:
$\begin{align}
& 3x+2=20 \\
& 3x=18 \\
& x=6
\end{align}$
Thus, the solution set $\left( x,y \right)$ to the system of equations is $\left( 6,-1 \right)$.
