1. College Algebra Chapter 5 Systems of Equations and Inequalities
Section 5.2
Systems of Linear Equations in Three Variables and Applications

2. Concepts
1. Identify Solutions to a System of Linear Equations in Three Variables
2. Solve Systems of Linear Equations in Three Variables
3. Use Systems of Linear Equations in Applications
4. Modeling with Linear Equations in Three Variables

3. Example 1:
Determine if the ordered triple is a solution to the system.

5. Concepts
1. Identify Solutions to a System of Linear Equations in Three Variables
2. Solve Systems of Linear Equations in Three Variables
3. Use Systems of Linear Equations in Applications
4. Modeling with Linear Equations in Three Variables

6. Example:
Solve.
Choose a pair of equations and eliminate one of the variables by using the addition method.
Choose a different pair of equations and eliminate the same variable.

7. Example continued:
You should now have two equations in two variables.
Solve this system by using the substitution or addition method.

8. Example continued:
Substitute the values of the variables found above into any of the three original equations that contain the third variable and solve for the third variable.

9. Example 2:
Solve.

10. Example 2 continued:

12. Example 3:
Solve.

13. Example 3 continued:

15. Example 4:
Solve.

16. Example 4 continued:

17. Example 5:
Solve.

20. Concepts
1. Identify Solutions to a System of Linear Equations in Three Variables
2. Solve Systems of Linear Equations in Three Variables
3. Use Systems of Linear Equations in Applications
4. Modeling with Linear Equations in Three Variables

21. Example 6:
The largest angle in a triangle measures 22° more than three times the smallest angle. The middle angle measures four more than the difference between the largest and smallest. Find the measures of the three angles.

22. Example 6 continued:

24. Concepts
1. Identify Solutions to a System of Linear Equations in Three Variables
2. Solve Systems of Linear Equations in Three Variables
3. Use Systems of Linear Equations in Applications
4. Modeling with Linear Equations in Three Variables

25. Example 7:
Find an equation of the form that defines a parabola through the points (1, 9), (–2, –24), (3, –19).

26. Example 7 continued:

27. Example 7 continued: