Lesson Systems of Equations. Elimination
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• Slide 1
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Systems of Equations Elimination

Combining Linear Equations

﻿A.REI.5

I CAN solve a system of equations by elimination. • Slide 2
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• Question 3
30 seconds
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Q.

I can combine 2 linear equations if the coefficients are not opposites.

True

False

• Question 4
120 seconds
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Q.

Solve by elimination:

3x+7y=23

-3x-7y=-17

No solution

ARN

(-3,3)

(3,3)

• Question 5
120 seconds
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Q.

Solve using elimination.

4x + 8y = 20

-4x + 2y = -30

(-7,1)

(2,-5)

(-2,5)

(7,-1)

• Slide 6
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Sometimes, the coefficients are NOT opposites, so we have to make them opposite...

How? We choose any variable, and multiply either (or both) equations to create a common multiple.

• Slide 7
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• Question 8
30 seconds
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Q.

For the following equations, which coefficients would be easier to make opposites?

2x + 3y = 12

4x - 7y = - 54

2x and 4x

3y and -7y

• Question 9
30 seconds
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Q.

Let's multiply the top equation by -2. What would be our new equation?

2x + 3y = 12

4x - 7y = - 54

4x - 6y = -24

-4x - 6y = 12

-4x - 6y = 24

-4x - 6y = -24

• Question 10
30 seconds
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Q.

Now, our equations will look like this

-4x - 6y = -24

4x - 7y = - 54

Let's combine (add) these 2 equations to ELIMINATE the x variable. What would our combined equations be?

-1y = 30

13y = -30

-1y = -78

-13y = -78

• Question 11
30 seconds
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Q.

Let's solve for y.

-13y = -78

y = 6

y = 1

y = 8

y = 30

• Question 12
30 seconds
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Q.

Now, let's find the solution to the system.

2x + 3y = 12

4x - 7y = - 54

(-3, 2)

(-3, -2)

(6, -3)

(-3, 6)

• Question 13
900 seconds
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Q.

﻿Solve by elimination

2x + 9y = -7

6x - 3y = 9

(-1, -1)

(2,-1)

(1,1)

(1,-1)

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