Solving Linear Systems with Matrices

We can solve systems of linear equations using determinants. Here, we learn how to solve the systems of two linear equations and systems of three linear equations. Such method is called Cramer's Rule for solving systems of linear equations.
   
Solving a System of Two Linear Equations in Two Variables Using Cramer's Rule

Let  ax + by = m
     cx + dy = n
be the general form of a system of two linear equations in two variables. To solve such a system using Cramer's rule, we must find the following determinants f ormed by the coefficients and constants in the system.