Elimination: Easy 0 Multiplications, Medium 1 Multiplication, Harder 2 Multiplication Problems
What
kind?
Easy – it’s all set up for you
already
Example
Equations
Side by Side
Observation There’s a
Make the
elimination
happen
Medium – One Multiplication is Harder – Two Multiplications
needed
are needed
and a
.
Elimination is all prepared for us already.
Consider the elimination:
 The terms are
and .
 Elimination will happen if we can
take
and turn it into
.
 Multiplication by
does it!
Just add the two equations together:
Multiply the first equation by
:
(
)
( )
Result of that + second equation:
-----------------------------------------------
Consider the elimination:
 The larger term is
 Can’t turn
into a
Consider the elimination:
 The larger term is
 Can’t turn
into a
So two multiplications are necessary
If you choose to eliminate the
 Coefficients are and
.
 Swap order:
and 4
 Change one sign:
and
Multiply first equation by – and
multiply second equation by
:
---------------------------------
Finish
solving the
system
First, we finish finding :
.
First, we finish finding :
.
First, we finish finding :
.
Then plug that into any equation that
contains both and . Solve for .
Then plug that into any equation that
contains both and . Solve for .
Then plug that into any equation that
contains both and . Solve for .
Final solution: (
Final solution: (
Final solution: (
)
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4Elimination012Mult.docx — 5/25/2012 6:28 PM – D.R.S.
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