Introduction to Solving Systems with Cramer’s Rule

Learning Objectives

By the end of this section, you will be able to:

  • Evaluate  2 × 2  determinants.
  • Use Cramer’s Rule to solve a system of equations in two variables.
  • Evaluate  3 × 3  determinants.
  • Use Cramer’s Rule to solve a system of three equations in three variables.
  • Know the properties of determinants.

We have learned how to solve systems of equations in two variables and three variables, and by multiple methods: substitution, addition, Gaussian elimination, using the inverse of a matrix, and graphing. Some of these methods are easier to apply than others and are more appropriate in certain situations. In this section, we will study two more strategies for solving systems of equations.