Answer
Solution set = $\{(1,-2)\}$
Work Step by Step
Rewrite the system:
$\left\{\begin{array}{l}
4x+y=2\\
2x-3y=8
\end{array}\right.$
$D= $determinant of the coefficient matrix
$=\left|\begin{array}{ll}
4 & 1\\
2 & -3
\end{array}\right|=4(-3)-(1)(2)=-14$
$D_{x}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
2 & 1\\
8 & -3
\end{array}\right|=-6-8=-14$
$D_{y}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
4 & 2\\
2 & 8
\end{array}\right|=32-4=28$
$x=\displaystyle \frac{D_{x}}{D}=\frac{-14}{-14}=1$
$y=\displaystyle \frac{D_{y}}{D}=\frac{28}{-14}=-2$
Solution set = $\{(1,-2)\}$
