1. Solving Systems Equations in Three Variables1
Steps 2
One Solution, Infinite Solutions, No Solution Scenarios 3
Practice Problems

2. Solving Systems Equations in Three Variables
Steps
Pick 2 equations
Use elimination to remove one variable
Pick another set of equations
Use elimination to eliminate the SAME variable
You now have 2 equations with 2 variables
Use elimination to solve the 2 new equations
You should now have 2 of the three variables solved
Substitute your 2 solutions into any of the original equations to solve for the third variable
Write solutions in ordered pair form

3. Solutions Key If you get three answers, there is one solution
If you get an answer of ‘a constant = same constant’ (0=0, 5=5, etc.), AND you can use elimination to solve the other two equations without getting a no solution case, there are infinite solutions
If you get a solution of ‘a constant = a different constant’ (0=3, 9=5, etc.), there are no solutions

4. One Solution

5. One Solution (Cont.)

6. One Solution (Cont.)

7. One Solution (Cont.)

8. Infinite Solutions

9. Infinite Solutions (Cont.)

10. No Solutions