dr. fowler ccm solving systems of equations by elimination – harder

Dr. Fowler CCM

Solving Systems of EquationsBy Elimination – Harder

Solving a system of equations by elimination using addition and subtraction.

Step 1: Put the equations in Standard Form.

Step 2: Determine which variable to eliminate.

Step 3: Add or subtract the equations.

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.

ALREADY IN NOTES – Read Only for Review

Elimination using Multiplication

1) Solve the system. Adding or subtracting will not eliminate

x + 2y = 6

3x + 3y = -6

But, we can multiply the first equationby -3 to eliminate the x term


x + 2y = 6

3x + 3y = -6

-3 ( )

1) Solve the system.


-3x + -6y = -18

3x + 3y = -6+-3y = -24

y = 8

ANS: (x, 8)

Be sure to distribute the -3to ALL in the equation.



x + 2y = 6

3x + 3y = -6

ANS: (x, 8)

Substitute y = 8 into equation

y =8

x + 2(8) = 6x + 16 = 6

x = -10



x + 2y = 6

3x + 3y = -6

Answer: ( -10 , 8)

Substitute y = 8 into equation

y =8x + 2(8) = 6

x + 16 = 6

x = -10


2) Solve the system:

2(2) + 2y = 6

4 + 2y = 6

2y = 2

y = 1

2x + 2y = 6

3x – y = 5

If we multiply the bottom

equation by 2 we can eliminate y:

2x + 2y = 6

(2)(3x – y = 5) 2x + 2y = 6(+) 6x – 2y = 10 8x = 16 x = 2

(2, 1)

Substitute x = 2 into either original equation:

More complex Problems

3x + 4y = -25

2x - 3y = 6

Multiply by 2

Multiply by -3.

This will get X’s to MATCH

3) Solve the system


3x + 4y = -25

2x - 3y = 6

2( )

-3( )

3) Solve the system


6x + 8y = -50

-6x + 9y = -18+17y = -68

y = -4

Answer: (x, -4)

3) Solve the system


3x + 4y = -25

2x - 3y = 6 Substitute y = -4

2x - 3(-4) = 62x - -12 = 6

2x + 12 = 6

2x = -6

x = -3 Answer: (-3, -4)

3) Solve the system

3x + 4y = -14x – 3y = 7

4) Solve the system using elimination.

3(1) + 4y = -1

3 + 4y = -1

4y = -4

y = -1

Multiply both equations

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

(4)(4x – 3y = 7)

9x + 12y = -3 (+) 16x – 12y = 28

25x = 25 x = 1

(1, -1)

Excellent Job !!!Well Done

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dr. fowler ccm solving systems of equations by elimination – harder

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