Using Addition w/ Multiplication to Solve a System 6-4
This is the same
method as Chapter 6-3, but to get ADDITIVE INVERSES of one variable you’ll need
to multiply one or both equations by a factor.
MULTIPLYING JUST
ONE EQUATION:
5x + 6y = -8
2x + 3y = -5
--------------------
Multiply either
the bottom by -2 to eliminate y:
5x + 6y = -8
-4x - 6y = 10
--------------------
x + 0 = 2
x = 2
MULTIPLYING BOTH
EQUATIONS:
4x + 2y = 8
3x + 3y = 9
--------------------
To eliminate x,
you’d need to multiply the top by 3 and the bottom by -4 so that you’d get 12x
and -12x
OR
Multiply the top
by 3 and the bottom by -2 so that you’d get 6y and -6y.
It’s your choice!
I think keeping
the numbers as small as possible is usually easier, so I’ll choose eliminating
y.
3(4x + 2y) = 3(8)
-2(3x + 3y) =
-2(9)
--------------------
12x + 6y = 24
-6x - 6y = -18
--------------------
6x + 0 = 6
x = 1
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