Solving System of Equations using Elimination

What does it mean to eliminate?

• To get rid of

• To combine

• To leave alone

What is the first thing you look for when using the elimination method

• Opposite Pairs

• Same Pairs

• Two Variables

Match the opposite pairs

• -2

• x

• -y

• y

• -4x

• 2x

• -14y

• 4x

• -x

• 14y

How do you eliminate opposite pairs in a system of equations?

• Add the equations together

• Subtract the equations

• Divide the equations

Answer explanation

The goal is to eliminate the opposite pairs, -4x + 4x = 0 therefore it is eliminated. Be sure to add together all other parts of the equation

How would the system of equations look below once you add the equations together?

5x + 4y = 10

-5x + 6y = 20

• 10y = 30

• 2y = 10

• 10x + 10y = 30

Solve the following system using elimination.

• (2,3)

• (6,-6)

• (4,6)

• (-6,3)

Answer explanation

Step 1: Add Equations together. The opposite pair of 4x and -4x are Eliminated. You are left with 6y = -36

Step 2: Solve 6y = -36 by dividing by 6 on both sides and y = -6

Step 3: Substitute y = -6 into one of the equations. I choose 4x + 8y = -24 because there are less negatives. This will look like 4x + 8(-6) = -24

Step 4: Solve for x

4x + 8(-6) = -24

4x -48 = -24 --> add 48 on both sides

• 4x = 24 --> divide by 4 on both sides

• x = 6

Solve the following system using elimination.

• (7,-1)

• (6,-6)

• (7,1)

• (-6,3)

Answer explanation

Step 1: Add Equations together. The opposite pair of 4x and -4x are Eliminated. You are left with 10y = -10

Step 2: Solve 10y = -10 by dividing by 10 on both sides and y = -1

Step 3: Substitute y = -1 into one of the equations. I choose 4x + 8y = 20 because there are no negatives. This will look like 4x + 8(-1) = 20

Step 4: Solve for x

4x + 8(-1) = 20 --> Multiply 8(-1)

4x - 8 = 20 --> add 8 on both sides

• 4x = 28 --> divide by 4 on both sides

• x = 7

Solve the following system using elimination.

• (-10,4)

• (4,7

• (10,-1)

• (-6,3)

Answer explanation

Step 1: Add Equations together. The opposite pair of -y and y are Eliminated. You are left with 3x = 30

Step 2: Solve 3x = 30 by dividing by 3 on both sides and x = 10

Step 3: Substitute x = 10 into one of the equations. I choose 2x + y = 19 because there are no negatives. This will look like 2(10) + y = 19

Step 4: Solve for y

2(10) + y = 19 --> multiply 2(10)

20 + y = 19 --> subtract 20 from both sides

y = -1

Solve the following system using elimination.

• (-1,-1)

• (6,-6)

• (1,4)

• (-6,3)

Answer explanation

Step 1: Add Equations together. The opposite pair of -6x and 6x are eliminiated. You are left with 9y = -9

Step 2: Solve 9y = -9 by dividing by 9 on both sides and y = -1

Step 3: Substitute y = -1 into one of the equations. I choose 6x + 4y = -10 because there are less negatives. This will look like 6x + 4(-1) = -10

Step 4: Solve for x

6x + 4(-1) = -10 --> multiply 4(-1)

6x - 4 = -10 --> add 4 to both sides

6x = -6 --> divide by 6 on both sides

x = -1

What is the solution to the system of equations below?

-x + 2y = 12

x + 6y = 20

• (-4, -6)

• (-4, 4)

• (2, 7)

• (8, 2)

Answer explanation

Step 1: Add Equations together. The opposite pair of -x and x are eliminiated. You are left with 8y = 32

Step 2: Solve 8y = 32 by dividing by 8on both sides and y = 4

Step 3: Substitute y = 4 into one of the equations. I choose x + 6y = 20 because there are less negatives. x + 6(4) = 20

Step 4: Solve for x

x + 24 = 20 --> subtract 24 on both sides

x = -4