Cramer’s rule is a way of solving a system of linear equations using determinants. - Math.net / wikipedia

From a system $Ax=b$ where the $n × n$ matrix A has a nonzero determinant, and the {\displaystyle \mathbf {x} =(x_{1},\ldots ,x_{n})^{\mathsf {T}}} {\displaystyle \mathbf {x} =(x_{1},\ldots ,x_{n})^{\mathsf {T}}}$ is the column vector of the variables. Then the theorem states that in this case the system has a unique solution, whose individual values for the unknowns are given by:

$x_{i}={\frac {\det(A_{i})}{\det(A)}}\qquad i=1,\ldots ,n$

where $ {\displaystyle A_{i}} A_{i} $ is the matrix formed by replacing the i-th column of A by the column vector b.

ex of application: Find Equation of Parabola Passing Through three Points

graphic equation