Answer
The solution of the system of equations is $\left( x,y \right)=\left( 8,-1 \right)$.
Work Step by Step
We have to simplify the system of equations:
$\begin{align}
& \frac{x-y}{3}=\frac{x+y}{2}-\frac{1}{2} \\
& 2x-2y=3x+3y-3
\end{align}$
That is,
$x+5y=3$ (I)
And,
$\begin{align}
& \frac{x+2}{2}-4=\frac{y+4}{3} \\
& 3x+6-24=2y+8
\end{align}$
And,
$3x-2y=26$ (II)
And multiply equation (I) by −3 to obtain:
$-3x-15y=-9$ (III)
And add equations (II) and (III):
$\begin{align}
& 3x-2y-3x-15y=26-9 \\
& -17y=17 \\
& y=-1
\end{align}$
Put the value $y=-1$ in equation (I):
$\begin{align}
& x-5=3 \\
& x=8
\end{align}$
