Answer
Solution set = $\{(-2,-1)\}$
Work Step by Step
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 = $\{(-2,-1)\}$
