Algebra 1 Notes

Lesson 7-3

Elimination Using Addition and Subtraction

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Mathematics Standards- Patterns, Functions and Algebra: Add, subtract,

multiply and divide monomials and polynomials.

- Patterns, Functions and Algebra: Solve real-world problems that can be modeled using linear, quadratic, exponential or square root functions.

- Patterns, Functions and Algebra: Solve and interpret the meaning of 2 by 2 systems of linear equations graphically, by substitution and by elimination, with and without technology.

- Patterns, Functions and Algebra: Solve real world problems that can be modeled using systems of linear equations and inequalities.

Vocabulary

Elimination – Third method to solve system of equations. Add or subtract equations.

First was Graphing.

Second was Substitution.

Example 1Use elimination to solve the system of equations.

-3x + 4y = 12

3x – 6y = 18

Example 1Use elimination to solve the system of equations.

-3x + 4y = 12

3x – 6y = 18

Example 1Use elimination to solve the system of equations.

-3x + 4y = 12

(+) 3x – 6y = 18

-2y =

Example 1Use elimination to solve the system of equations.

-3x + 4y = 12

(+) 3x – 6y = 18

-2y = 30

-2 -2

y = -15

Example 1Use elimination to solve the system of equations.

-3x + 4y = 12

(+) 3x – 6y = 18

-2y = 30

-2 -2

y = -15

Example 1Use elimination to solve the system of equations.

-3x + 4y = 12 -3x + 4(-15) = 12

(+) 3x – 6y = 18

-2y = 30

-2 -2

y = -15

Example 1Use elimination to solve the system of equations.

-3x + 4y = 12 -3x + 4(-15) = 12

(+) 3x – 6y = 18 -3x – 60 = 12

-2y = 30

-2 -2

y = -15

Example 1Use elimination to solve the system of equations.

-3x + 4y = 12 -3x + 4(-15) = 12

(+) 3x – 6y = 18 -3x – 60 = 12

-2y = 30 +60 +60

-2 -2

y = -15

Example 1Use elimination to solve the system of equations.

-3x + 4y = 12 -3x + 4(-15) = 12

(+) 3x – 6y = 18 -3x – 60 = 12

-2y = 30 +60 +60

-2 -2 -3x = 72

y = -15

Example 1Use elimination to solve the system of equations.

-3x + 4y = 12 -3x + 4(-15) = 12

(+) 3x – 6y = 18 -3x – 60 = 12

-2y = 30 +60 +60

-2 -2 -3x = 72

y = -15 -3 -3

Example 1Use elimination to solve the system of equations.

-3x + 4y = 12 -3x + 4(-15) = 12

(+) 3x – 6y = 18 -3x – 60 = 12

-2y = 30 +60 +60

-2 -2 -3x = 72

y = -15 x = -24 -3 -3

Example 1Use elimination to solve the system of equations.

-3x + 4y = 12 -3x + 4(-15) = 12

(+) 3x – 6y = 18 -3x – 60 = 12

-2y = 30 +60 +60

-2 -2 (-24, -15) -3x = 72

y = -15 x = -24 -3 -3

Example 2Use elimination to solve the system of equations.

4x + 2y = 28

4x – 3y = 18

Example 2Use elimination to solve the system of equations.

4x + 2y = 28

4x – 3y = 18

Example 2Use elimination to solve the system of equations.

4x + 2y = 28

(–) 4x – 3y = 18

5y =

Example 2Use elimination to solve the system of equations.

4x + 2y = 28

(–) 4x – 3y = 18

5y = 10

Example 2Use elimination to solve the system of equations.

4x + 2y = 28

(–) 4x – 3y = 18

5y = 10

5 5

y = 2

Example 2Use elimination to solve the system of equations.

4x + 2y = 28

(–) 4x – 3y = 18

5y = 10

5 5

y = 2

Example 2Use elimination to solve the system of equations.

4x + 2y = 28 4x + 2(2) = 28

(–) 4x – 3y = 18

5y = 10

5 5

y = 2

Example 2Use elimination to solve the system of equations.

4x + 2y = 28 4x + 2(2) = 28

(–) 4x – 3y = 18 4x + 4 = 28

5y = 10

5 5

y = 2

Example 2Use elimination to solve the system of equations.

4x + 2y = 28 4x + 2(2) = 28

(–) 4x – 3y = 18 4x + 4 = 28

5y = 10 – 4 – 4

5 5

y = 2

Example 2Use elimination to solve the system of equations.

4x + 2y = 28 4x + 2(2) = 28

(–) 4x – 3y = 18 4x + 4 = 28

5y = 10 – 4 – 4

5 5 4x = 24

y = 2

Example 2Use elimination to solve the system of equations.

4x + 2y = 28 4x + 2(2) = 28

(–) 4x – 3y = 18 4x + 4 = 28

5y = 10 – 4 – 4

5 5 4x = 24

y = 2 4 4

x = 6

Example 2Use elimination to solve the system of equations.

4x + 2y = 28 4x + 2(2) = 28

(–) 4x – 3y = 18 4x + 4 = 28

5y = 10 – 4 – 4

5 5 4x = 24

y = 2 4 4

(6, 2) x = 6

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n – 3m

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n – 3m = 12

2n

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n – 3m = 12

2n + 3m

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n – 3m = 12

2n + 3m = 6

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n – 3m = 12

2n + 3m = 6

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n – 3m = 12

(+) 2n + 3m = 6

6n = 18

6 6

n = 3

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n – 3m = 12

(+) 2n + 3m = 6

6n = 18

6 6

n = 3

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n – 3m = 12 4(3) – 3m = 12

(+) 2n + 3m = 6

6n = 18

6 6

n = 3

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n – 3m = 12 4(3) – 3m = 12

(+) 2n + 3m = 6 12 – 3m = 12

6n = 18

6 6

n = 3

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n – 3m = 12 4(3) – 3m = 12

(+) 2n + 3m = 6 12 – 3m = 12

6n = 18 – 12 – 12

6 6

n = 3

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n – 3m = 12 4(3) – 3m = 12

(+) 2n + 3m = 6 12 – 3m = 12

6n = 18 – 12 – 12

6 6 -3m = 0

n = 3

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n – 3m = 12 4(3) – 3m = 12

(+) 2n + 3m = 6 12 – 3m = 12

6n = 18 – 12 – 12

6 6 -3m = 0

n = 3 m = 0

Example 3Four times one number minus three times another number is 12. Two times the first number added to three times the second number is 6. Find the numbers.

4n – 3m = 12 4(3) – 3m = 12

(+) 2n + 3m = 6 12 – 3m = 12

6n = 18 – 12 – 12

6 6 -3m = 0

n = 3 3 and 0 m = 0

Example 42x + 3y = 7

7x + 2y = 32

Example 42x + 3y = 7

7x + 2y = 32

Uh Oh……

Example 42x + 3y = 7

7x + 2y = 32

Uh Oh……

We will learn how to solve these in the next section.

Homework

Pg. 385

12-32 (evens)

34,35, and 40