1. Linear Programming WKST
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3-6: Three Variable Systems

2. Linear Programming WKST
12/9/2018 2:00 PM
3-6: Three Variable Systems

3. Linear Programming WKST
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3-6: Three Variable Systems

4. Section 3.4, ©2011, dangjim@gmail.com
3-Variable Systems
Section 3.4,
©2011,
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3-6: Three Variable Systems

5. Briefing of 3-variable systems:
Graphing in two dimensional y + – + – x
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3-6: Three Variable Systems

6. Briefing of 3-variable systems:
Graphing in three dimensional + – + x – + y – z
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3-6: Three Variable Systems

7. 3-6: Three Variable Systems
Video
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3-6: Three Variable Systems

8. 3-6: Three Variable Systems
Example 1
Solve:
HINT: Look at the third equation (z = 3) and work backwards.
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3-6: Three Variable Systems

9. 3-6: Three Variable Systems
Example 1
Solve:
z = 3
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3-6: Three Variable Systems

10. 3-6: Three Variable Systems
Your Turn
Solve:
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3-6: Three Variable Systems

11. Steps in 3-variable systems
Choose any two equations and eliminate one variable using elimination
Choose two OTHER equations and eliminate the SAME variable using elimination
With the two new equations, eliminate another variable
Substitute the one variable in an equation in STEP 3
Substitute the two variables into any equation given
Check the solution
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3-6: Three Variable Systems

12. Steps in 3-step variables
Eliminate
Eliminate
Eliminate
Substitute in Step 3
Substitute in any equation
Check
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3-6: Three Variable Systems

13. 3-6: Three Variable Systems
Example 2
Solve:
Choose any two equations and eliminate one variable using elimination
Getting rid of x
(1) +
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3-6: Three Variable Systems

14. 3-6: Three Variable Systems
Example 2
Solve:
2. Choose two OTHER equations and eliminate the SAME variable using elimination
Getting rid of x
(2) +
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3-6: Three Variable Systems

15. 3-6: Three Variable Systems
Example 2
Solve:
2. Choose two OTHER equations and eliminate the SAME variable using elimination
(2) + +
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3-6: Three Variable Systems

16. 3-6: Three Variable Systems
Example 2
Solve:
3. With the two new equations, eliminate another variable using elimination
(–1) + +
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3-6: Three Variable Systems

17. Doesn’t matter which equation to choose 3-6: Three Variable Systems
Example 2
Solve:
4. Substitute to an equation in STEP 3 +
Doesn’t matter which equation to choose
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3-6: Three Variable Systems

18. 3-6: Three Variable Systems
Example 2
Solve:
5. Substitute the two variables into any equation given
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3-6: Three Variable Systems

19. 3-6: Three Variable Systems
Example 2
Solve:
6. Check the solution
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3-6: Three Variable Systems

20. 3-6: Three Variable Systems
Example 3
Solve:
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3-6: Three Variable Systems

21. 3-6: Three Variable Systems
Example 3
Solve:
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3-6: Three Variable Systems

22. 3-6: Three Variable Systems
Example 4
Solve:
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3-6: Three Variable Systems

23. 3-6: Three Variable Systems
Your Turn
Solve:
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3-6: Three Variable Systems

24. 3-6: Three Variable Systems
Example 5
Solve:
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3-6: Three Variable Systems

25. 3-6: Three Variable Systems
Example 6
Solve:
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3-6: Three Variable Systems

26. 3-6: Three Variable Systems
Your Turn
Solve:
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3-6: Three Variable Systems

27. 3-6: Three Variable Systems
Assignment
Worksheet
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3-6: Three Variable Systems