Cramer's rule

Cramer’s rule is a simple little rule that lets us use determinants to solve a system of linear equations.

The rule says that you can solve for any variable in the system by calculating

where is the determinant of the coefficient matrix with the answer column values in the variable column you’re trying to solve, and where is the determinant of the coefficient matrix.

Which means that if we want to find and we need to find and respectively.

Two unknowns §

Given the linear system of two equations in two unknowns,

we can say that

where

Three unknowns §

Given the linear system of three quations in three unknowns,

we can say that

where