## College Algebra (6th Edition)

Solution set = $\displaystyle \{(2,\frac{1}{2})\}$
$D=$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 = $\displaystyle \{(2,\frac{1}{2})\}$