1. Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Multivariable Linear Systems (Section 7-3)

2. Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solving Using Back Substitution If you are given a system of equations in which one equation has 3 variables, one equation has 2 of those variables, and the third equation has 1 variable, you should solve by plugging the known variable into the equation with 2 variables. This will give you 2 variables, to complete solving plug the 2 known variables into the equation with 3 variables.

3. Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solve the system of equations. Example 1 x – 2y + 3z = 9 y + 4z = 7 z = 2

4. Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solve the system of equations. Example 2 x + y – 3z = -1 -y – z = 0 -x + 2y = 1

5. Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Elimination Method to Solve a System in Three Variables 1)Use the elimination method to rewrite the system as a linear system in two variables. 2) Solve the system of two equations for both of the variables. 3) Subsitute the two values found in step 2 into one of the equations and solve for the last variable.

6. Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solve the system of equations. Example 3 x – 2y + 3z = 9 -x + 3y + z =-2 2x – 5y + 5z = 17

7. Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solve the system of equations. Example 4

8. Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solve the system of equations. Example 5 x + y – z = 3 2x – y – z = 1 x + y – 2z = 5

9. Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Solve the system of equations. Example 6 x – 3y + z = 1 2x - y - 2z = 2 x + 2y – 3z = -1

10. Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Use Cramer’s Rule to solve the linear system. Example 7

11. Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. Use Cramer’s Rule to solve the linear system. Example 8

12. Essential Question: How do you solve a system of 3 equations? Students will write a summary of the steps for solving a system of 3 equations. HW #43 pg 505-506 (1, 7, 15-25 odd)