Question

Cramers Rule? I am confused

Answer 1

$D$ is the determinant of the coefficient matrix:

$D=\begin{vmatrix}3&-1\\-3&5\end{vmatrix}=3\times5-(-1)\times(-3)=12$

$D_x$ is the determinant of the coefficient matrix, but this time you replace the $x$-coefficients with the values on the right hand side of the equations:

$D_x=\begin{vmatrix}-1&-1\\13&5\end{vmatrix}=(-1)\times5-(-1)\times13=\boxed{8}$