1. Elimination Method! Lesson 2.9 (y do I have to get rid of x?) ‘In Common’ Ballad: http://youtu.be/Br7qn4yLf-Ihttp://youtu.be/Br7qn4yLf-I ‘All I do is solve’ Rap: http://youtu.be/1qHTmxlaZWQhttp://youtu.be/1qHTmxlaZWQ

2. Concept: Solving Systems of Equations Essential Question: How can I manipulate equation(s) to solve a system of equations? (standards REI 5-6, 10-11) Vocabulary: Elimination/Algebraically/Linear Combination Method

3. Example 1 Solve the following system by elimination.

4. 1.Write your equations so that the corresponding variables are aligned. Notice 2x is above x and -3y is above 3y

5. 2. Check to see if the same variable has the same coefficient. The coefficients y differ only by a sign. 3. Multiply to make the coefficients the same value, but different signs. Our example has 3y and -3y so we can move on to step 4.

6. 4. Use addition to eliminate one of the variables. 5. Solve for the variable. 3x = 0 x = 0

7. 6. Continue solving the system to find the remaining variable. Using an original equation, substitute the value you found for y.

8. 7. Write the solution as a point.

9. 1.Write your equations so that the corresponding variables are aligned. Notice x is above 3x and 4y is above 2y Example 2: x + 4y = 0 3x + 2y = 20

10. 2. Check to see if the same variable has the same coefficient. Example 2: The coefficients are different for x and y. x + 4y = 0 3x + 2y = 20

11. 3. Multiply to make the coefficients the same value, but different signs. x + 4y = 0 3x + 2y = 20 How can we make the coefficients of x the same but with different signs? -3(x + 4y = 0) 3x + 2y = 20 - 3x - 12y = 0 3x + 2y = 20

12. 4. Use addition to eliminate one of the variables. 5. Solve for the variable. - 3x - 12y = 0 + 3x + 2y = 20 -10y = 20 y = -2

13. 6. Continue solving the system to find the remaining variable. Using an original equation, substitute the value you found for y. x + 4y = 0 x + 4(-2) = 0 x – 8 = 0 x = 8

14. Solution: (8, -2) 7. Write the solution as a point.

15. Notice 2x is above 3x and 3y is above 4y Example 3: 1.Write your equations so that the corresponding variables are aligned. 2x + 3y = 9 3x + 4y = 15

16. 2. Check to see if the same variable has the same coefficient. Example 3: The coefficients for x and y are not the same. 2x + 3y = 9 3x + 4y = 15

17. 3. Use multiplication or division to make one of the variables have the same coefficient but different signs. How can we make the coefficients of x the same but with different signs? 2x + 3y = 9 3x + 4y = 15 3(2x + 3y = 9) -2(3x + 4y = 15) 6x + 9y = 27 -6x – 8y = -30

18. 4. Use addition to eliminate one of the variables. 5. Solve for the variable (we can skip this step because the variable is already solved). y = -3 6x + 9y = 27 -6x – 8y = -30 y = -3

19. 6. Continue solving the system to find the remaining variable. Using an original equation, substitute the value you found for y. 2x + 3y = 9 2x + 3(-3) = 9 2x – 9 = 9 2x = 18 x = 9

20. Solution: (9, 3) 7. Write the solution as a point.

21. You Try!

24. You Try Challenge!

25. Each word is worth 10 cents. Write a summary describing how to solve a system using the elimination method.