Unit 3, Lesson 5

Steps to Use Substitution Method to Solve a System with 3 Equations

1. Isolate a variable in one of the equations. 2. Substitute that value in each of the other equations. 3. Solve for remaining variables. 4. Check the solution in all 3 of the original equations. Write the solution as an ordered triple.

Steps to Use Elimination Method to Solve a System with 3 Equations

1. Rewrite the system as two smaller systems, each containing two of the three equations (first & second and first & third equation). 2. Eliminate the same variable in each of the two smaller systems. 3. Write the resulting equations in two variables together as a system of equations. Solve the system for the remaining variables. 4. Substitute the value of the variables from the system of two equations in one of the original equations with three variables. 5. Check the solution in all 3 of original equations. Write the solution as an ordered triple.

Solutions of a System with 3 Equations

Ordered triple - (x, y, z) Must be a solution of all 3 equations