2. Solving Systems of Equations in Three Variables

3. Ordered Triple- The solution of a system of equations in three variables x,y, and z written as (x, y, z) VOCABULARY

4. One Solution Infinitely Many Solutions No Solutions See page 145 for diagram NUMBER OF SOLUTIONS

5. Used to find number of solutions in a system of equations with three variables ELIMINATION METHOD

6. Pick a variable to get rid of Take two of the equations and use elimination to go down to two variables Take a different pair of equations and repeat process Now you have two equations in two variables Solve like we did earlier in chapter for those two variables Solve for third variable at the end STEPS FOR SOLVING

7. 2x – 1y + 3z = -2 1x + 4y – 2z = 16 5x + 1y – 1z = 14 ONE SOLUTION

8. WORK PAGE

9. 3x + 1y + 1z = 0 -1x + 2y – 2z = -3 4x – 1y – 3z = 9 ONE SOLUTION

10. WORK PAGE

11. OTHER EXAMPLES

12. 8x + 12y – 24z = -40 3x – 8y +12z = 23 2x + 3y - 6z = -10 INFINITELY MANY SOLUTIONS

13. WORK PAGE

14. 3x – 2y + 4z = 8 -6x + 4y – 8z = -16 1x + 2y – 4z = 4 INFINITELY MANY SOLUTIONS

15. WORK PAGE

16. OTHER EXAMPLES

17. 8x +4y – 3z = 7 4x + 2y – 6z = -15 10x + 5y – 15z = -25 NO SOLUTIONS

18. WORK PAGE

19. 4x – 3y – 2z =8 1x + 5y + 3z = 9 -8x + 6y + 4z = 2 NO SOLUTIONS

20. WORK PAGE

21. OTHER EXAMPLES

22. Problem 22 & 23 on page 150 WORD PROBLEMS

23. WORK PAGE

24. #24 on page 150 WORD PROBLEMS

25. WORK PAGE

26. Worksheet 3-5 HOMEWORK

27. Pages 154-156 11-32 all CHAPTER REVIEW