1. Systems of Equations in Two and Three Variables
Advanced Math Topics
Mrs. Mongold

2. Solving Systems By Elimination
Choose a variable and get the coefficients to be opposites, then add the equations and solve for remaining value. Plug answer back in for second solution.

7. Remember Always check you solutions in BOTH equations!!
Answers should be written as ordered pair
If a system has at least one solution it is consistent
If a system has no solution it is inconsistent
Dependent equations are when all the ordered pairs for one equation satisfy the other equation

8. Three Variables… same but different
3 Patterns for a solution
1- Consistent, when three planes have a single point in common or when three planes intersect in a line

9. Three Variables… same but different
3 Patterns for a solution
1- Consistent, when three planes have a single point in common or when three planes intersect in a line
2-Inconsistent, when three planes intersect at no common points

10. Three Variables… same but different
3 Patterns for a solution
1- Consistent, when three planes have a single point in common or when three planes intersect in a line
2-Inconsistent, when three planes intersect at no common points
3-Dependent, when three planes coincide at all points

11. To Solve 3 variable systems
Use elimination or substitution methods to get a system with two variables and then follow the rules for two variable systems

12. Example

13. Example

14. Example

15. Homework

16. Homework