1. Solve Systems of Linear Equations in Three Variables
Notes 3.5 (Day 2)
Solve Systems of Linear Equations in Three Variables

2. The Linear Combination (Elimination) Method for a 3-variable System
Step 1: Find the easiest variable to eliminate.
Step 2: Eliminate that variable two times using different equations. (you may have to multiply the equations to make the variables cancel)
Step 3: Use the two new equations to make a linear system with two variables.
Step 4: Pick the easiest variable to eliminate in the new system of equations.
Step 5: Eliminate that variable. (you may have to multiply the equations to make the variables cancel)
Step 6: Solve for the remaining variable.
Step 7: Plug in the solution to the two variable system and solve for another variable.
Step 8: Plug in the two solved variables into one of the three given equations
** If there is already a variable missing in one of the equations, use the other two equations to eliminate that variable again.

3. Solve the system using the elimination method.

4. Solve the system using the elimination method.

5. Solve the system using the elimination method.

6. Remember:
If you obtain an answer such as 0 = 1, then the system has no solution.
If you obtain an answer such as 3 = 3, then the system has infinitely many solutions.

7. Homework:
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