Solving Systems of Equations By Elimination

Warm – up!!

*As you walk in, please pick up your calculator!!* Use substitution to solve the following systems of equations.

1. x – 3 = y 2y + 7x = 42. 6x -8 = 3y 18 = 7y + 4x

Solving Systems of Equations

So far, we have solved systems using graphing and substitution. Today we are adding another tool to our toolbox called ELIMINATION.

Our goal for elimination is to cancel out one of our variables so that we only have one variable left to solve for.

Solving a system of equations by elimination.

Step 1: Put the equations in Standard Form.

Step 2: Determine which variable to eliminate.

Step 3: Eliminate the variable and solve.

Step 4: Plug back in to find the other variable.

Step 5: Check your solution.

Standard Form: Ax + By = C

Look for variables that have thesame coefficient.

Solve for the variable.

Substitute the value of the variableinto the equation.

Substitute your ordered pair intoBOTH equations.

1) Solve the system using elimination.

2x + 2y = 63x – 2y = 4

Step 1: Put the equations in Standard Form.

Step 2: Determine which variable to eliminate.

They already are!

Look at my ys! What coefficients do they both

have?

1) Solve the system using elimination.

Step 4: Plug back in to find the other variable.

2(2) + 2y = 64 + 2y = 6

2y = 2y = 1

2x + 2y = 63x – 2y = 4

Step 3: Eliminate the variable and solve.

2x + 2y = 6 3x – 2y = 4 5x = 10 x = 2

2x + 2y = 6(+) 3x – 2y = 4

1) Solve the system using elimination.

Step 5: Check your solution.

(2, 1)2(2) + 2(1) = 63(2) - 2(1) = 4

2x + 2y = 63x – 2y = 4

A great way to know if you have the right answer!!

2) Solve the system using elimination.

-4x + 4y = 74x – 3y = 9

Step 1: Put the equations in Standard Form. They already are!

Step 2: Determine which variable to eliminate.

Which variable has the same coefficient?

2) Solve the system using elimination.

-4x + 4y = 154x – 3y = 9

Step 4: Plug back in to find the other variable.

x + 4(2) = 7x + 8 = 7

x = -1

Eliminate one of the variables! -4x + 4y = 15 4x – 3y = 9 y = 2

-4x + 4y = 15 (+) 4x – 3y = 9

12y = 24

Step 3: Multiply the equations and solve.

-4x + 4y = 154x – 3y = 9

2) Solve the system using elimination.

Step 5: Check your solution.

(-1, 2)-4(-1) + 4(2) =154(-1) - 3(2) = 9

What is the first step when solving with elimination?

Plug numbers into the equation.

Add or subtract the equations.

Solve for a variable.

Check your answer.

Determine which variable to eliminate.

Put the equations in standard form.

Put the steps of solving by

elimination in order!!

Which variable is easier to eliminate?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

3x - 4y = 44x + 4y = 6

1. x2. y3. 64. 4

3) Solve the system using elimination.

3x + 7y = -284x – 7y = 7

Step 1: Put the equations in Standard Form. They already are!

Step 2: Determine which variable to eliminate.

You try!!

What variable is easiest to eliminate?

3x + 7y = -284x – 7y = 7

3) Solve the system using elimination.

Step 4: Plug back in to find the other variable.

3(-3) + 7y = -28-9 + 7y = -28

7y = -37y = -37/7

Step 3: Multiply the equations and solve.

Eliminate a variable!!!! 3x + 7y = -284x – 7y = 7 x = - 3

3x + 7y = -28 (+) 4x – 7y = 7 7x = -21

3x + 7y = -284x – 7y = 7

3) Solve the system using elimination.

Step 5: Check your solution.

(-3, -37/7)3(-3) + 7(-37/7) = -28

4(-3) - 7(-37/7) = 7

Solve using elimination.

2x – 3y = 1-2x - 4y = 6

1. (2, 1)2. (1, -2)3. (5, 3)4. (-1, -1)

You try!!