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Elimination Method! Lesson 2.9 (y do I have to get rid of x?) ‘In Common’ Ballad:...
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Transcript of Elimination Method! Lesson 2.9 (y do I have to get rid of x?) ‘In Common’ Ballad:...
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Solving systems…..
Elimination Method!Lesson 2.9(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
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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
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Example 1Solve the following system by elimination.
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1.Write your equations so that the corresponding variables are aligned.
Notice 2x is above x and -3y is above 3y
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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.
![Page 6: Elimination Method! Lesson 2.9 (y do I have to get rid of x?) ‘In Common’ Ballad: //youtu.be/Br7qn4yLf-I ‘All I do is solve’](https://reader036.fdocuments.us/reader036/viewer/2022081603/56649f145503460f94c2952e/html5/thumbnails/6.jpg)
4. Use addition to eliminate one of the variables.
5. Solve for the variable .
3x = 0 x = 0
![Page 7: Elimination Method! Lesson 2.9 (y do I have to get rid of x?) ‘In Common’ Ballad: //youtu.be/Br7qn4yLf-I ‘All I do is solve’](https://reader036.fdocuments.us/reader036/viewer/2022081603/56649f145503460f94c2952e/html5/thumbnails/7.jpg)
6. Continue solving the system to find the remaining variable.
Using an original equation, substitute the value you found for y.
-3y = -11 y =
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Solution: (0, 3
7. Write the solution as a point.
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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 = 03x + 2y = 20
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2. Check to see if the same variable has the same coefficient.
Example 2:
The coefficients are different for x and y.
x + 4y = 03x + 2y = 20
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3. Multiply to make the coefficients the same value, but different signs.
x + 4y = 03x + 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
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4. Use addition to eliminate one of the variables.
5. Solve for the variable .
- 3x - 12y = 0 + 3x + 2y = 20 -10y = 20
-10y = 20 y = -2
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6. Continue solving the system to find the remaining variable.
Using an original equation, substitute the value you found for y.
x + 4y = 0x + 4(-2) = 0x – 8 = 0 x = 8
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Solution: (8, -2)
7. Write the solution as a point.
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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 = 93x + 4y = 15
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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 = 93x + 4y = 15
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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 = 93x + 4y = 15
3(2x + 3y = 9)-2(3x + 4y = 15) 6x + 9y = 27-6x – 8y = -30
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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
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6. Continue solving the system to find the remaining variable.
Using an original equation, substitute the value you found for y.
2x + 3y = 92x + 3(-3) = 92x – 9 = 9 2x = 18 x = 9
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Solution: (9, 3)
7. Write the solution as a point.
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You Try!
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You Try!
2
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You Try!
3
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You Try Challenge!4.
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$2.00 Summary….
Each word is worth 10 cents. Write a summary describing how to solve a system using the elimination method.