For the system $a_1x+b_1y=c_1$, $a_2x+b_2y=c_2$, Cramer's rule gives

For two linear equations in two unknowns, Cramer's rule states $x=\frac{D_1}{D}$ and $y=\frac{D_2}{D}$, provided $D\ne 0$. Here $D$ is the determinant of coefficients and $D_1,D_2$ are obtained by replacing the respective variable columns by constants.