This document discusses solving systems of linear equations in three variables. It provides examples of eliminating variables to solve such systems and applications involving determining values for a, b, and c given x and y variable data points. One example involves determining values for a, b, and c using data about the distance a car travels in seconds after the brakes are applied.

1. Section 5.2 Systems of Linear Equations in Three Variables

2. Systems of Linear Equations in Three Variables and Their Solutions

4. Example

5. Solving Systems of Linear Equations in Three Variables by Eliminating Variables

7. Example

8. Applications

9. In applications the data given is often the x and y values of the variables and you are to determine the values of a,b,c – a triple. See below example 4 from your textbook.

10. Example 108 3 68 2 32 1 Y, feet car travels once the brakes are applied X,seconds in motion after breaks are applied

11. (a) (b) (c) (d)