Mathematics · important
Cramer's rule for two variables for JEE
Test of consistency and solution of simultaneous linear equations in two or three variables using matrices
Formula
For \(a_1x+b_1y+c_1=0,\ a_2x+b_2y+c_2=0\), with \(D=\begin{vmatrix}a_1&b_1\\a_2&b_2\end{vmatrix}\), \(D_x=\begin{vmatrix}-c_1&b_1\\-c_2&b_2\end{vmatrix}\), \(D_y=\begin{vmatrix}a_1&-c_1\\a_2&-c_2\end{vmatrix}\), then \(x=\dfrac{D_x}{D},\ y=\dfrac{D_y}{D}\).
Variables: \(D\): determinant of coefficients.
Conditions: \(D\ne 0\).
Direct solution of 2-variable linear equations.