Answer
Solution set = $\displaystyle \{(2,\frac{1}{2})\}$
Work Step by Step
$D= $determinant of the coefficient matrix
$=\left|\begin{array}{ll}
1 & 2\\
3 & -4
\end{array}\right|=1(-4)-(2)(3)=-10$
$D_{x}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
3 & 2\\
4 & -4
\end{array}\right|=-12-8=-20$
$D_{y}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
1 & 3\\
3 & 4
\end{array}\right|=4-9=-5$
$x=\displaystyle \frac{D_{x}}{D}=\frac{-20}{-10}=2$
$y=\displaystyle \frac{D_{y}}{D}=\frac{-5}{-10}=\frac{1}{2}$
Solution set = $\displaystyle \{(2,\frac{1}{2})\}$
