Metode Cramer

Metode Cramer

Metode Cramer digunakan menyelesaikan sistem persamaan linier

\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:

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