Answer
$\{(-2,-5)\}$
Work Step by Step
We are given the system of equations:
$\begin{cases}
4x+3y=-23\\
3x-5y=19
\end{cases}$
Compute $D,D_x,D_y,D_z$:
$D=\begin{vmatrix}4&3\\3&-5\end{vmatrix}=4(-5)-3(3)=-29$
$D_x=\begin{vmatrix}-23&3\\19&-5\end{vmatrix}=-23(-5)-3(19)=58$
$D_y=\begin{vmatrix}4&-23\\3&19\end{vmatrix}=4(19)-3(-23)=145$
Determine $x$:
$x=\dfrac{D_x}{D}=\dfrac{58}{-29}=-2$
Determine $y$:
$y=\dfrac{D_y}{D}=\dfrac{145}{-29}=-5$
The solution set is:
$\{(-2,-5)\}$
