## College Algebra (6th Edition)

Solution set = $\{(-2,-1)\}$
Rewrite the system: $\left\{\begin{array}{l} 3x-7y=1\\ 2x-3y=-1 \end{array}\right.$ $D=$determinant of the coefficient matrix $=\left|\begin{array}{ll} 3 & -7\\ 2 & -3 \end{array}\right|=3(-3)-(-7)(2)=5$ $D_{x}=$ in D, replace the x column with the constants column $=\left|\begin{array}{ll} 1 & -7\\ -1 & -3 \end{array}\right|=-3-7=-10$ $D_{y}=$ in D, replace the x column with the constants column $=\left|\begin{array}{ll} 3 & 1\\ 2 & -1 \end{array}\right|=-3-2=-5$ $x=\displaystyle \frac{D_{x}}{D}=\frac{-10}{5}=-2$ $y=\displaystyle \frac{D_{y}}{D}=\frac{-5}{5}=-1$ Solution set = $\{(-2,-1)\}$