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

Dr. Fowler CCM

Solving Systems of EquationsBy Elimination – Easier

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.

1) Solve the system using elimination.

x + y = 5

3x – y = 7Step 1: Put the equations in

Standard Form.

Step 2: Determine which variable to eliminate.

They already are!

The y’s have the same

coefficient.

Step 3: Add or subtract the equations.

Add to eliminate y.

x + y = 5

(+) 3x – y = 7

4x = 12

x = 3

1) Solve the system using elimination.

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

x + y = 5

(3) + y = 5

y = 2

Step 5: Check your solution.

(3, 2)

(3) + (2) = 5

3(3) - (2) = 7

The solution is (3, 2). What do you think the answer would be if you solved using substitution?

x + y = 5

3x – y = 7

EXAMPLE #2:

STEP 2: Use subtraction to eliminate 5x. 5x + 3y =11 5x + 3y = 11

-(5x - 2y =1) -5x + 2y = -1

5x + 3y = 11

5x = 2y + 1

Note: the (-) is distributed.

STEP 3: Solve for the variable. 5x + 3y =11

-5x + 2y = -15y =10 y = 2

STEP1: Write both equations in Ax + By = C form. 5x + 3y =11 5x - 2y =1

STEP 4: Solve for the other variable by substitutingy = 2 into either equation.5x + 3y =11

5x + 3(2) =11 5x + 6 =11 5x = 5 x = 1

5x + 3y = 11

5x = 2y + 1

The solution to the system is (1, 2).

3) Solve the system using elimination.

4x + y = 7

4x – 2y = -2Step 1: Put the equations in

Standard Form.They already are!

Step 2: Determine which variable to eliminate.

The x’s have the same

coefficient.

Step 3: Add or subtract the equations.

Subtract to eliminate x.

4x + y = 7

(-) 4x – 2y = -2

3y = 9

y = 3Remember to “keep-change-

change”

3) Solve the system using elimination.

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

4x + y = 7

4x + (3) = 7

4x = 4

x = 1

Step 5: Check your solution.

(1, 3)

4(1) + (3) = 7

4(1) - 2(3) = -2

4x + y = 7

4x – 2y = -2

4) Solve the system using elimination.

y = 7 – 2x

4x + y = 5Step 1: Put the equations in

Standard Form.2x + y = 7

4x + y = 5

Step 2: Determine which variable to eliminate.

The y’s have the same

coefficient.

Step 3: Add or subtract the equations.

Subtract to eliminate y.

2x + y = 7

(-) 4x + y = 5

-2x = 2

x = -1

4) Solve the system using elimination.

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

y = 7 – 2x

y = 7 – 2(-1)

y = 9

Step 5: Check your solution.

(-1, 9)

(9) = 7 – 2(-1)

4(-1) + (9) = 5

y = 7 – 2x

4x + y = 5

Elimination using Addition

5) Solve the system

x - 2y = 5

2x + 2y = 7

Lets add both equations to each other

Elimination using Addition

5) Solve the system

x - 2y = 5

2x + 2y = 7

Lets add both equations to each other+

NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

Elimination using Addition

5) Solve the system

x - 2y = 5

2x + 2y = 7

Lets add both equations to each other+

3x = 12x = 4

ANS: (4, y)

NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

Elimination using Addition

5) Solve the system

x - 2y = 5

2x + 2y = 7

ANS: (4, y)

Lets substitute x = 4 into this equation.

4 - 2y = 5 Solve for y - 2y = 1

y = 12

NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

Elimination using Addition

5) Solve the system

x - 2y = 5

2x + 2y = 7

Answer: (4, )

Lets substitute x = 4 into this equation.

4 - 2y = 5 Solve for y - 2y = 1

y = 12 1

2

NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

Elimination using Addition

3x + y = 14

4x - y = 7

NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

5) Solve the system

Elimination using Addition

3x + y = 14

4x - y = 7

7x = 21x = 3

ANS: (3, y)

+

5) Solve the system

Elimination using Addition

Answer: (3, 5 )

3x + y = 14

4x - y = 7

Substitute x = 3 into this equation

3(3) + y = 149 + y = 14

y = 5

NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

5) Solve the system

Excellent Job !!!Well Done

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