Metode Cramer digunakan menyelesaikan sistem persamaan linear

\begin{equation*} \begin{split} ax + by & = p\\ cx + dy & = q\\ \end{split} \end{equation*}

Sistem persamaan dapat ditulis sebagai:

\(\begin{pmatrix}a & b \\ c & d \end{pmatrix} \begin{pmatrix}x \\ y \end{pmatrix} = \begin{pmatrix} {\color {blue} p} \\ {\color {blue} q} \end{pmatrix}\)

Nilai x dan y dapat ditentukan dengan:

\(x = \dfrac {D_x}{D} = \dfrac{\begin{vmatrix} {\color {blue} p} & b  \\ {\color {blue} q} & d\end{vmatrix}}{\begin{vmatrix}a & b \\ c & d \end{vmatrix}} \quad \quad y = \dfrac {D_y}{D} = \dfrac{\begin{vmatrix}a & {\color {blue} p} \\c & {\color {blue} q} \end{vmatrix}}{\begin{vmatrix}a & b \\ c & d \end{vmatrix}} \)

Contoh

\(3x + 2y = 4\)

\(2x - y = 5\)

\(x = \dfrac {D_x}{D} = \dfrac{\begin{vmatrix} {\color {blue} 4} & 2 \\ {\color {blue} 5} & -1\end{vmatrix}}{\begin{vmatrix}3 & 2 \\ 2 & -1 \end{vmatrix}} = \dfrac {-4 - 10}{-3 - 4} = \dfrac {-14}{-7} = 2\)

\(y = \dfrac {D_y}{D} = \dfrac{\begin{vmatrix}3 & {\color {blue} 4} \\ 2 & {\color {blue} 5}\end{vmatrix}}{\begin{vmatrix}3 & 2 \\ 2 & -1 \end{vmatrix}} = \dfrac {15 - 8}{-3 - 4} = \dfrac {7}{-7} = -1\)