These equations correspond to the matrix equation
\(\begin{pmatrix} 5&3\\2&4\end{pmatrix}\begin{pmatrix} x\\y\end{pmatrix} = \begin{pmatrix} -11\\-10\end{pmatrix}\)
The determinant of the coefficient matrix is
\(|A| = \begin{vmatrix}5&3\\2&4\end{vmatrix}\)
\(= (5) (4) - (3) (2)\)
\(= 20 - 6\)
\(= 14\)
By Cramer's rule
\(x = \frac{\begin{vmatrix}-11&3\\-10&4\end{vmatrix}}{|A|}\)
\(=\frac{(-44+30)}{14}\)
\(=\frac{-14}{14}\)
\(=-1\)
\(y = \frac{\begin{vmatrix}5&-11\\2&-10\end{vmatrix}}{|A|}\)
\(=\frac{(-50 +22)}{14}\)
\(=\frac{-28}{14}\)
\(=-2\)
