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5-3 Elimination Using Addition and Subtraction

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Title: 5-3 Elimination Using Addition and Subtraction


1
5-3 Elimination Using Addition and Subtraction
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
2
When solving a linear system by substitution, you
needed to isolate one of the variables. Sometimes
it is not easy to isolate one of the variables.
What is the result when you try to isolate one of
the variables in the system below?
3
When it is not easy to isolate one of the
variables using the substitution method, it may
be easier to solve the system by elimination.
When using this method, you will be adding the
two equations together in order to eliminate one
of the variables.
4
Elimination Using Addition
Add the equations if one of the variables has
opposites. Then solve.
Substitute the solved value into either of the
original equations to find the value for the
other variable.
Write the solution as an ordered pair.
Check by substitution in both original equations.
(4,3)
5
Use elimination to solve the system of equations.
Example 2
Example 3
Example 1
(1,2)
(2,3)
(3,5)
6
When the coefficients of terms are the same, you
can eliminate the terms by subtracting the
equations.
When using elimination with subtraction to solve
systems of equations, do not forget to distribute
the negative sign over the entire equation that
is subtracted. Since subtraction is the same as
adding the inverse, you should change the signs
of the terms and then add to eliminate the
variable.
7
Elimination Using Subtraction
Subtract the equations if one of the variables
have the same coefficients. Then solve.
-
-
-
Substitute the solved value into either of the
original equations to find the value for the
other variable.
Write the solution as an ordered pair.
Check by substitution in both original equations.
(4,-7)
8
Elimination Using Subtraction
Distribute the negative sign over the entire
equation that is subtracted.
-


It will not matter which equation you create the
opposite!
(-1,2)
9
Use elimination to solve the system of equations.
Example 5
Example 4
-

-
-
-
-
(2,6)
10
Write and Solve a System of Equations
Twice one number added to another number is 18.
Four times the first number minus the other
number is 12. Find the numbers.
Assign Labels.
Let x first number Let y second number
Translate each sentence.
Solve the system.
Write a sentence to give the answer.
The numbers are 5 and 8.
11
Example 6 The sum of two numbers is -10.
Negative three times the first number minus the
second number equals 2. Find the numbers.
Example 7 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.
Assign labels.
Translate each sentence.
Solve the system.
Write a sentence to give the answer.
12
Example 6 The sum of two numbers is -10.
Negative three times the first number minus the
second number equals 2. Find the numbers.
Let x first number Let y second number
Translate each sentence.
Solve the system.
Write a sentence to give the answer.
The numbers are 4 and -14.
13
Example 7 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.
Let x first number Let y second number
Translate each sentence.
Solve the system.
Write a sentence to give the answer.
The numbers are 3 and 0.
14
Homework
5-A5 Page 269-270 722,33-34,42-45.
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