Answer
$\{(2,-1)\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
x-2y=4\\
3x+2y=4
\end{cases}$
Compute $D,D_x,D_y$:
$D=\begin{vmatrix}1&-2\\3&2\end{vmatrix}=1(2)-3(-2)=8$
$D_x=\begin{vmatrix}4&-2\\4&2\end{vmatrix}=4(2)-4(-2)=16$
$D_y=\begin{vmatrix}1&4\\3&4\end{vmatrix}=1(4)-3(4)=-8$
Determine $x$:
$x=\dfrac{D_x}{D}=\dfrac{16}{8}=2$
Determine $y$:
$y=\dfrac{D_y}{D}=\dfrac{-8}{8}=-1$
The solution set is:
$\{(2,-1)\}$
