1. Chapter 3 Examples Section 5 Solving System of Equations Algebraically with 3 variables

2. Objective You will explore ways of solving systems of equations algebraically with 3 variables and strategize which is best based on the given problem.

3. Systems of Equations with 3 Variables ●Systems of equations with 2 variables are linear functions. ●Systems of equations with 3 variables are planes.

4. Solutions One Solution: The 3 Planes Intersect at One Point Infinite Solutions: The 3 Planes Intersect at One Line

5. Solutions No Solution: All 3 Planes Do Not Intersect each other No Solution: All 3 Planes Do Not Intersect each other

6. Algebraic Techniques Choose one Variable to isolate – choose one variable that will be the easiest to eliminate from all 3 equations. Use one equation with the other 2 to eliminate the variable you chose to get rid of. Elimination - use addition, subtraction, or multiplication to eliminate one of the variables from all 3 equations. Then solve for the remaining remaining 2x2 system. Now solve the 2 remaining equations for one of the variables. Once you find and answer substitute it back into one of the new 2x2 systems to solve for the other variable. Then take both values and substitute them into one of the ORIGINAL equations to find the 3 rd and last variable.

7. Solve the system of equations. Choose an equation to pair with the other 2. You can use any equation. 5x + 3y + 2z = 2 2x + y - z = 5 x + 4y + 2z = 16 Example 1 (-2, 6, -3)

8. Example 2 Solve the system of equations. 2x + y - 3z = 5 x + 2y - 4z = 7 6x + 3y - 9z = 15 Infinite number of solutions.

9. Example 3 Solve the system of equations. 3x - y - 2z = 4 6x + 4y + 8z = 11 9x + 6y + 12z = 15 There is No Solution for this system

10. Homework ●pg 142; 13-25 odd, 27, 28