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Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

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Page 1: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

Objective

The student will be able to:

solve systems of equations using elimination with multiplication.

Designed by Skip Tyler, Varina High School

Page 2: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

Solving Systems of Equations

So far, we have solved systems using graphing, substitution, and elimination. These notes go one step further and show how to use ELIMINATION with multiplication.

What happens when the coefficients are not the same?

We multiply the equations to make them the same! You’ll see…

Page 3: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

Solving a system of equations by elimination using multiplication.

Step 1: Put the equations in Standard Form.

Step 2: Determine which variable to eliminate.

Step 3: Multiply the equations 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 the

same coefficient.

Solve for the variable.

Substitute the value of the variable

into the equation.

Substitute your ordered pair into

BOTH equations.

Page 4: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

1) Solve the system using elimination.

2x + 2y = 6

3x – y = 5Step 1: Put the equations in

Standard Form.

Step 2: Determine which variable to eliminate.

They already are!

None of the coefficients are the same!

Find the least common multiple of each variable.

LCM = 6x, LCM = 2y

Which is easier to obtain?

2y(you only have to multiplythe bottom equation by 2)

Page 5: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

1) Solve the system using elimination.

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

2(2) + 2y = 6

4 + 2y = 6

2y = 2

y = 1

2x + 2y = 6

3x – y = 5

Step 3: Multiply the equations and solve.

Multiply the bottom equation by 2

2x + 2y = 6

(2)(3x – y = 5)

8x = 16

x = 2

2x + 2y = 6(+) 6x – 2y = 10

Page 6: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

1) Solve the system using elimination.

Step 5: Check your solution.

(2, 1)

2(2) + 2(1) = 6

3(2) - (1) = 5

2x + 2y = 6

3x – y = 5

Solving with multiplication adds one more step to the elimination process.

Page 7: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

2) Solve the system using elimination.

x + 4y = 7

4x – 3y = 9Step 1: Put the equations in

Standard Form.They already are!

Step 2: Determine which variable to eliminate.

Find the least common multiple of each variable.

LCM = 4x, LCM = 12y

Which is easier to obtain?

4x(you only have to multiplythe top equation by -4 to

make them inverses)

Page 8: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

2) Solve the system using elimination.

x + 4y = 7

4x – 3y = 9

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

x + 4(1) = 7

x + 4 = 7

x = 3

Step 3: Multiply the equations and solve.

Multiply the top equation by -4

(-4)(x + 4y = 7)

4x – 3y = 9)

y = 1

-4x – 16y = -28 (+) 4x – 3y = 9

-19y = -19

Page 9: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

2) Solve the system using elimination.

Step 5: Check your solution.

(3, 1)

(3) + 4(1) = 7

4(3) - 3(1) = 9

x + 4y = 7

4x – 3y = 9

Page 10: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

What is the first step when solving with elimination?

1. Add or subtract the equations.

2. Multiply the equations.

3. Plug numbers into the equation.

4. Solve for a variable.

5. Check your answer.

6. Determine which variable to eliminate.

7. Put the equations in standard form.

Page 11: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

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 + y = 44x + 4y = 6

1. x

2. y

3. 6

4. 4

Page 12: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

3) Solve the system using elimination.

3x + 4y = -1

4x – 3y = 7

Step 1: Put the equations in Standard Form.

They already are!

Step 2: Determine which variable to eliminate.

Find the least common multiple of each variable.

LCM = 12x, LCM = 12y

Which is easier to obtain?

Either! I’ll pick y because the signs are already opposite.

Page 13: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

3) Solve the system using elimination.

3x + 4y = -1

4x – 3y = 7

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

3(1) + 4y = -1

3 + 4y = -1

4y = -4

y = -1

Step 3: Multiply the equations and solve.

Multiply both equations

(3)(3x + 4y = -1)

(4)(4x – 3y = 7)

x = 1

9x + 12y = -3 (+) 16x – 12y = 28

25x = 25

Page 14: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

3) Solve the system using elimination.

Step 5: Check your solution.

(1, -1)

3(1) + 4(-1) = -1

4(1) - 3(-1) = 7

3x + 4y = -1

4x – 3y = 7

Page 15: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

What is the best number to multiply the top equation by to eliminate the x’s?

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 + y = 46x + 4y = 6

1. -4

2. -2

3. 2

4. 4

Page 16: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

Solve using elimination.

2x – 3y = 1x + 2y = -3

1. (2, 1)

2. (1, -2)

3. (5, 3)

4. (-1, -1)

Page 17: Objective The student will be able to: solve systems of equations using elimination with multiplication. Designed by Skip Tyler, Varina High School

Find two numbers whose sum is 18 and whose difference 22.

1. 14 and 4

2. 20 and -2

3. 24 and -6

4. 30 and 8