Metode Cramer digunakan menyelesaikan sistem persamaan linear

$$\begin{array}{rl}ax+by& =p\\ cx+dy& =q\end{array}$$

Sistem persamaan dapat ditulis sebagai:

$\left(\begin{array}{cc}a& b\\ c& d\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}p\\ q\end{array}\right)$

Nilai x dan y dapat ditentukan dengan:

$x={\displaystyle \frac{D_x}{D}}={\displaystyle \frac{\left|\begin{array}{cc}p& b\\ q& d\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}}y={\displaystyle \frac{D_y}{D}}={\displaystyle \frac{\left|\begin{array}{cc}a& p\\ c& q\end{array}\right|}{\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|}}$

Contoh

$3x+2y=4$

$2x-y=5$

$x={\displaystyle \frac{D_x}{D}}={\displaystyle \frac{\left|\begin{array}{cc}4& 2\\ 5& -1\end{array}\right|}{\left|\begin{array}{cc}3& 2\\ 2& -1\end{array}\right|}}={\displaystyle \frac{-4-10}{-3-4}}={\displaystyle \frac{-14}{-7}}=2$

$y={\displaystyle \frac{D_y}{D}}={\displaystyle \frac{\left|\begin{array}{cc}3& 4\\ 2& 5\end{array}\right|}{\left|\begin{array}{cc}3& 2\\ 2& -1\end{array}\right|}}={\displaystyle \frac{15-8}{-3-4}}={\displaystyle \frac{7}{-7}}=-1$