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Algebra 1 Notes
Lesson 7-3
Elimination Using Addition and Subtraction
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Did you turn in your homework?
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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.
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Vocabulary
Elimination – Third method to solve system of equations. Add or subtract equations.
First was Graphing.
Second was Substitution.
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Example 1Use elimination to solve the system of equations.
-3x + 4y = 12
3x – 6y = 18
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Example 1Use elimination to solve the system of equations.
-3x + 4y = 12
3x – 6y = 18
![Page 7: Algebra 1 Notes Lesson 7-3 Elimination Using Addition and Subtraction](https://reader036.vdocuments.net/reader036/viewer/2022062401/5a4d1b077f8b9ab0599889e2/html5/thumbnails/7.jpg)
Example 1Use elimination to solve the system of equations.
-3x + 4y = 12
(+) 3x – 6y = 18
-2y =
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Example 1Use elimination to solve the system of equations.
-3x + 4y = 12
(+) 3x – 6y = 18
-2y = 30
-2 -2
y = -15
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Example 1Use elimination to solve the system of equations.
-3x + 4y = 12
(+) 3x – 6y = 18
-2y = 30
-2 -2
y = -15
![Page 10: Algebra 1 Notes Lesson 7-3 Elimination Using Addition and Subtraction](https://reader036.vdocuments.net/reader036/viewer/2022062401/5a4d1b077f8b9ab0599889e2/html5/thumbnails/10.jpg)
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
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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
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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
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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
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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
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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
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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
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Example 2Use elimination to solve the system of equations.
4x + 2y = 28
4x – 3y = 18
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Example 2Use elimination to solve the system of equations.
4x + 2y = 28
4x – 3y = 18
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Example 2Use elimination to solve the system of equations.
4x + 2y = 28
(–) 4x – 3y = 18
5y =
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Example 2Use elimination to solve the system of equations.
4x + 2y = 28
(–) 4x – 3y = 18
5y = 10
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Example 2Use elimination to solve the system of equations.
4x + 2y = 28
(–) 4x – 3y = 18
5y = 10
5 5
y = 2
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Example 2Use elimination to solve the system of equations.
4x + 2y = 28
(–) 4x – 3y = 18
5y = 10
5 5
y = 2
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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Example 42x + 3y = 7
7x + 2y = 32
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Example 42x + 3y = 7
7x + 2y = 32
Uh Oh……
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Example 42x + 3y = 7
7x + 2y = 32
Uh Oh……
We will learn how to solve these in the next section.
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Homework
Pg. 385
12-32 (evens)
34,35, and 40