SOLVING SYSTEMS OF LINEAR EQUATIONS BY ELIMINATION Section 17.3.
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Transcript of SOLVING SYSTEMS OF LINEAR EQUATIONS BY ELIMINATION Section 17.3.
SOLVING SYSTEMS OF LINEAR EQUATIONS BY ELIMINATION
Section 17.3
Using the Elimination Method
The elimination method utilizes the addition property of equality:
For example
If and , then .A B C D A C B D
If , then .A B A C B C or
Still adding the same thing to both sides since C = D.
&
Using the Elimination Method
Consider the system
7
5
x y
x y
A = B
C = D
A+C=B+D
Using the Elimination Method
Consider the system Consider the system
7
5
x y
x y
2 0 12x y 2 12x
6x
2 11
3 13
x y
x y
4 3 24x y
Uh oh. Cannot solve an
equation in two variables.
Adding worked because one variable had
opposite coefficients and thus added to zero and was eliminated.
Using the Elimination Method
For elimination to work, one of the variables must have opposite coefficients. If not, you can use the multiplication property to
change the coefficients.
This method is also called linear combination, or addition.
Using the Elimination Method
Consider the system
Solve using addition by eliminating either variable. Multiply the equations by any value that will produce
opposite coefficients on either variable. Must multiply one entire equation by the same value, but can use a different value for the other equation.
2 11
3 13
x y
x y
2 11
3 13
x y
x y
-3( ) ( )-3
3 6 33
3 13
x y
x y
5 20y 4y
Substitute to get x = 3
2 11
3 13
x y
x y
-2( )
( )-2
2 11
6 2 26
x y
x y
5 15x 3x
Substitute to get y = -4
OR