Transcript 3x - Elgin Local Schools

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 1
Use elimination to solve the system of
equations.
-3x + 4y = 12
3x – 6y = 18
Example 1
Use elimination to solve the system of
equations.
-3x + 4y = 12
3x – 6y = 18
Example 1
Use elimination to solve the system of
equations.
-3x + 4y = 12
(+) 3x – 6y = 18
-2y =
Example 1
Use elimination to solve the system of
equations.
-3x + 4y = 12
(+) 3x – 6y = 18
-2y = 30
-2
-2
y = -15
Example 1
Use elimination to solve the system of
equations.
-3x + 4y = 12
(+) 3x – 6y = 18
-2y = 30
-2
-2
y = -15
Example 1
Use elimination to solve the system of
equations.
-3x + 4y = 12
(+) 3x – 6y = 18
-2y = 30
-2
-2
y = -15
-3x + 4(-15) = 12
Example 1
Use 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 1
Use 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 1
Use 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
-3x = 72
Example 1
Use 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
-3x = 72
-3
-3
Example 1
Use 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
-3x = 72
x = -24
-3
-3
Example 1
Use 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
(-24, -15) -3x = 72
x = -24
-3
-3
Example 2
Use elimination to solve the system of
equations.
4x + 2y = 28
4x – 3y = 18
Example 2
Use elimination to solve the system of
equations.
4x + 2y = 28
4x – 3y = 18
Example 2
Use elimination to solve the system of
equations.
4x + 2y = 28
(–) 4x – 3y = 18
5y =
Example 2
Use elimination to solve the system of
equations.
4x + 2y = 28
(–) 4x – 3y = 18
5y = 10
Example 2
Use elimination to solve the system of
equations.
4x + 2y = 28
(–) 4x – 3y = 18
5y = 10
5
5
y=2
Example 2
Use elimination to solve the system of
equations.
4x + 2y = 28
(–) 4x – 3y = 18
5y = 10
5
5
y=2
Example 2
Use elimination to solve the system of
equations.
4x + 2y = 28
(–) 4x – 3y = 18
5y = 10
5
5
y=2
4x + 2(2) = 28
Example 2
Use 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 2
Use 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
–4
–4
Example 2
Use elimination to solve the system of
equations.
4x + 2y = 28
4x + 2(2) = 28
(–) 4x – 3y = 18
4x + 4 = 28
5y = 10
–4
5
4x = 24
5
y=2
–4
Example 2
Use elimination to solve the system of
equations.
4x + 2y = 28
4x + 2(2) = 28
(–) 4x – 3y = 18
4x + 4 = 28
5y = 10
–4
5
4x = 24
5
y=2
4
–4
4
x=6
Example 2
Use elimination to solve the system of
equations.
4x + 2y = 28
4x + 2(2) = 28
(–) 4x – 3y = 18
4x + 4 = 28
5y = 10
–4
5
4x = 24
5
y=2
4
(6, 2)
–4
4
x=6
Example 3
Four 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 3
Four 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 3
Four 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 3
Four 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 3
Four 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 3
Four 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 3
Four 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 3
Four 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 3
Four 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
4(3) – 3m = 12
Example 3
Four 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
4(3) – 3m = 12
12 – 3m = 12
Example 3
Four 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
4(3) – 3m = 12
12 – 3m = 12
– 12
– 12
Example 3
Four 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
4(3) – 3m = 12
12 – 3m = 12
– 12
– 12
-3m = 0
Example 3
Four 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
4(3) – 3m = 12
12 – 3m = 12
– 12
– 12
-3m = 0
m=0
Example 3
Four 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
4(3) – 3m = 12
12 – 3m = 12
– 12
6
n=3
– 12
-3m = 0
3 and 0
m=0
Example 4
2x + 3y = 7
7x + 2y = 32
Example 4
2x + 3y = 7
7x + 2y = 32
Uh Oh……
Example 4
2x + 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