1. Warm UP: Solve the following systems of equations:
1) y = 3x ) 3x + y = 6
3x – y = x + y = 3
3) 5x – 2y = 4
3x + y = 9

2. Solving Systems in 3 Variables
1.5 Notes

3. What is a 3 variable system?
Typically, is has three equations with three different variables to solve for, x, y and z. There are at least two ways to solve these systems.

4. How do we do this?
Step 1: Reduce the system to two equations in two variables (substitution or elimination)
Step 2: Solve the resulting system of two equations with two variables
Step 3: Substitute your solution into one of the equations found in step 1
Step 4: Substitute both solutions into one of the original equations, solve for the remaining variable.

5. EX 1: EX 2:
x + z = x – 2y – 4z = 3
x + y + 2z = x + 3y + 2z = -3
x + 2y + z = x + 5y + 3z = 3

6. Solve the following 3 variable system:
1) 2x + 3y + 7z = 13
3x + 2y - 5z = -22
5x + 7y – 3z = -28

7. Your turn:
1) 2x - 4y + 3z = 17
x + 2y – z = 0
4x – y - z = 6