Solving Linear Systems by Elimination

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

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

Let's solve for y.

-13y = -78

• y = 6

• y = 1

• y = 8

• y = 30

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

2x + 3y = 12

4x - 7y = - 54

• (-3, 2)

• (-3, -2)

• (6, -3)

• (-3, 6)

Your Turn:

Solve by elimination

2x + 9y = -7

6x - 3y = 9

• (-1, -1)

• (2,-1)

• (1,1)

• (1,-1)