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

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

Video http://www.youtube.com/watch?v=ova8GSmPV4o&safety_mode=true&persist_safety_mode=1

Example 1 Solve the following system by elimination.

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

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.

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

6. Continue solving the system to find the remaining variable 6. Continue solving the system to find the remaining variable. Using an original equation, substitute the value you found for y. 𝟐 𝟎 −𝟑𝒚=−𝟏𝟏 -3y = -11 y = 𝟏𝟏 𝟑 =𝟑 𝟐 𝟑

7. Write the solution as a point.

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

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

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

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

6. Continue solving the system to find the remaining variable 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

7. Write the solution as a point.

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

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

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

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

6. Continue solving the system to find the remaining variable 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

7. Write the solution as a point.

You Try! 𝟏. 𝟒𝒙−𝟑𝒚=−𝟐𝟔 𝒙+𝟑𝒚=𝟏

You Try! 2. 𝟕𝒙+𝟐𝒚=𝟏𝟖 𝟑𝒙+𝟐𝒚=𝟐

You Try! 3. 𝟑𝒙−𝟐𝒚=𝟐 𝟓𝒙−𝟓𝒚=𝟏𝟎

You Try Challenge! 4. 𝒙=𝟐𝒚 −𝟏𝟐 𝟑𝒙+𝟖𝒚=𝟑𝟒

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