Cramer's rule uses the concept of determinant of a matrix. As a general rule, given the equations [latex]A_{1}[/latex]x + [latex]B_{1}[/latex]y = [latex]C_{1}[/latex] and [latex]A_{2}[/latex]x + [latex]B_{2}[/latex]y = [latex]C_{2}[/latex], then : D = [latex]\begin{pmatrix}A_{1} & B_{1}\\A_{2} & B_{2}\end{pmatrix}[/latex] = A[latex]_{1}[/latex]× B[latex]_{2}[/latex] – A[latex]_{2}[/latex]× B[latex]_{1}[/latex] D[latex]_{1}[/latex] = [latex]\begin{pmatrix}C_{1} & B_{1}\\C_{2} & B_{2}\end{pmatrix}[/latex] = C[latex]_{1}[/latex]× B[latex]_{2}[/latex] – B[latex]_{1}[/latex]× C[latex]_{2}[/latex] D[latex]_{2}[/latex] = [latex]\begin{pmatrix}A_{1} & C_{1}\\A_{2} & C_{2}\end{pmatrix}[/latex] = A[latex]_{1}[/latex]× C[latex]_{2}[/latex] – A[latex]_{2}[/latex]× C[latex]_{1}[/latex] x = [latex]\dfrac{D_{1}}{D}[/latex] where D ≠ 0 and  y = [latex]\dfrac{D_{2}}{D}[/latex] where D ≠ 0