Systems of Equations. Elimination

Systems of Equations Elimination

Combining Linear Equations

A.REI.5

I CAN solve a system of equations by elimination.

***VERY IMPORTANT SLIDE***

Multiple Choice

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

• True

• False

Multiple Choice

Solve by elimination:

3x+7y=23

-3x-7y=-17

• No solution

• ARN

• (-3,3)

• (3,3)

Multiple Choice

Solve using elimination.

4x + 8y = 20

-4x + 2y = -30

• (-7,1)

• (2,-5)

• (-2,5)

• (7,-1)

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.

Poll

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

2x + 3y = 12

4x - 7y = - 54

• 2x and 4x

• 3y and -7y

Multiple Choice

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

Multiple Choice

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

Multiple Choice

Let's solve for y.

-13y = -78

• y = 6

• y = 1

• y = 8

• y = 30

Multiple Choice

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

2x + 3y = 12

4x - 7y = - 54

• (-3, 2)

• (-3, -2)

• (6, -3)

• (-3, 6)

Multiple Choice

Your Turn:

Solve by elimination

2x + 9y = -7

6x - 3y = 9

• (-1, -1)

• (2,-1)

• (1,1)

• (1,-1)