Systems of Equations. Elimination

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

Solve by elimination:

3x+7y=23

-3x-7y=-17

Solve using elimination.

4x + 8y = 20

-4x + 2y = -30

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

2x + 3y = 12

4x - 7y = - 54

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

2x + 3y = 12

4x - 7y = - 54

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?

Let's solve for y.

-13y = -78

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

2x + 3y = 12

4x - 7y = - 54

Your Turn:

Solve by elimination

2x + 9y = -7

6x - 3y = 9