Answer
Solution set = $\{(-1,-3)\}$
Work Step by Step
$D= $determinant of the coefficient matrix
$=\left|\begin{array}{ll}
1 & -2\\
5 & -1
\end{array}\right|=1(-1)-(-2)(5)=9$
$D_{x}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
5 & -2\\
-2 & -1
\end{array}\right|=-5-4=-9$
$D_{y}=$ in D, replace the x column with the constants column
$=\left|\begin{array}{ll}
1 & 5\\
5 & -2
\end{array}\right|=-2-25=-27$
$x=\displaystyle \frac{D_{x}}{D}=\frac{-9}{9}=-1$
$y=\displaystyle \frac{D_{y}}{D}=\frac{-27}{9}=-3$
Solution set = $\{(-1,-3)\}$
