Answer
$\left\{\left(2,-1\right)\right\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
x-2y-4=0\\
3x+2y-4=0
\end{cases}$
Bring the system to the standard form:
$\begin{cases}
x-2y=4\\
3x+2y=4
\end{cases}$
Use the elimination method. Add the two equations to eliminate $y$ and find $x$:
$x-2y+3x+2y=4+4$
$4x=8$
$x=2$
Substitute $x=2$ in the first equation of the given system and determine $y$:
$x-2y=4$
$2-2y=4$
$2y=-2$
$y=-1$
The solution set is:
$\left\{\left(2,-1\right)\right\}$
