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
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
• http://www.youtube.com/watch?v=ova8GSmPV4o&safety_mo
de=true&persist_safety_mode=1
Example 1
Solve the following system by elimination.
ì2x - 3y = -11
í
î x + 3y = 11
1. Write your equations so that the
corresponding variables are aligned.
ì2x - 3y = -11
í
î x + 3y = 11
Notice 2x
is above x
and -3y is
above 3y
2. Check to see if the same variable has the
same coefficient.
ì2x - 3y = -11
í
î x + 3y = 11
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.
The coefficients
y differ only by a
sign.
4. Use addition to eliminate one of the
variables.
2x - 3y = -11
x + 3y = 11
3x + 0 =
5. Solve for the variable .
3x = 0
x=0
0
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
𝟏𝟏
𝟐
y= =𝟑
𝟑
𝟑
7. Write the solution as a point.
Solution: (0,
𝟐
3 )
𝟑
Example 2:
1. 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:
x + 4y = 0
3x + 2y = 20
The coefficients
are different for x
and y.
3. Multiply to make the coefficients the same
value, but different signs.
x + 4y = 0
3x + 2y = 20
-3(x + 4y = 0)
3x + 2y = 20
- 3x - 12y = 0
3x + 2y = 20
How can we make
the coefficients of x
the same but with
different signs?
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.
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.
Solution: (8, -2)
Example 3:
1. Write your equations so that the
corresponding variables are aligned.
2x + 3y = 9
3x + 4y = 15
Notice 2x
is above 3x
and 3y is
above 4y
2. Check to see if the same variable has the
same coefficient.
Example 3:
2x + 3y = 9
3x + 4y = 15
The coefficients
for x and y are
not the same.
3. Use multiplication or division to make one of
the variables have the same coefficient but
How can we make
different signs.
2x + 3y = 9
3x + 4y = 15
3(2x + 3y = 9)
-2(3x + 4y = 15)
6x + 9y = 27
-6x – 8y = -30
the coefficients of x
the same but with
different signs?
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.
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.
Solution: (9, 3)
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
Each word is worth 10 cents. Write a summary
describing how to solve a system using the
elimination method.