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Jojo Manzo
science forum beginner
Joined: 03 May 2005
Posts: 1
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 Posted: Tue May 03, 2005 7:22 pm Post subject:
Need Help Solving FOUR Unknowns
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I have THREE problems, with FOUR unknowns in each, is there any way I
can solve them , I assume I may get more than one set of possible
answers, can anyone help?
6s + 6d + 9a + 10p = 20
10s + 9d + 5a + 6p = 30
16s + 15d + 14a + 16p = 50
Do I need to create a Matrix to solve this? This is not a homework
assignment, I am trying to see how certain game figures are rated in a
minature game and I can't make heads or tails of it!
Thanks
jojomanzo@gmail.com |
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Bart Goddard
science forum beginner
Joined: 24 Mar 2005
Posts: 43
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| Posted: Tue May 03, 2005 7:33 pm Post subject:
Re: Need Help Solving FOUR Unknowns
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jojomanzo@gmail.com wrote:
| Quote: | 6s + 6d + 9a + 10p = 20
10s + 9d + 5a + 6p = 30
16s + 15d + 14a + 16p = 50
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Note that the 3rd equation is the sum of the other two,
so you have only 2 equations. In this case, you can
choose any two of your variables and choose any values
you like for them. This reduces the system to a 2x2
system, which will be much easier to solve.
Bart |
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Karl-Olav Nyberg
science forum beginner
Joined: 03 May 2005
Posts: 9
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| Posted: Tue May 03, 2005 7:48 pm Post subject:
Re: Need Help Solving FOUR Unknowns
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"Jojo Manzo" <jojomanzo@gmail.com> skrev i melding
news:1115155333.076605.109190@g14g2000cwa.googlegroups.com...
| Quote: | I have THREE problems, with FOUR unknowns in each, is there any way I
can solve them , I assume I may get more than one set of possible
answers, can anyone help?
6s + 6d + 9a + 10p = 20
10s + 9d + 5a + 6p = 30
16s + 15d + 14a + 16p = 50
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You actually only got two equations. The third one is just adding equation
one and two.
..
| Quote: |
Do I need to create a Matrix to solve this? This is not a homework
assignment, I am trying to see how certain game figures are rated in a
minature game and I can't make heads or tails of it!
Thanks
jojomanzo@gmail.com
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Karl-Olav Nyberg |
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Arturo Magidin
science forum Guru
Joined: 25 Mar 2005
Posts: 1838
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| Posted: Tue May 03, 2005 9:46 pm Post subject:
Re: Need Help Solving FOUR Unknowns
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In article <1115155333.076605.109190@g14g2000cwa.googlegroups.com>,
Jojo Manzo <jojomanzo@gmail.com> wrote:
| Quote: | I have THREE problems, with FOUR unknowns in each, is there any way I
can solve them , I assume I may get more than one set of possible
answers, can anyone help?
6s + 6d + 9a + 10p = 20
10s + 9d + 5a + 6p = 30
16s + 15d + 14a + 16p = 50
|
Third equation is the sum of the first two, so it can be discarded.
| Quote: |
Do I need to create a Matrix to solve this? This is not a homework
assignment, I am trying to see how certain game figures are rated in a
minature game and I can't make heads or tails of it!
|
You don't have to create a matrix, but it helps. You have a system of
2 linear equations in 4 unknowns. There will be either no solutions,
or an infinite number of solutions. Since it is just two equations and
the left hand sides are not multiples of each other, there will be an
infinite number of solutions.
Take the expanded matrix of the system,
( 6 6 9 10 | 20 )
(10 9 5 6 | 30 )
Multiplying the first row by 5 and the second by 3 gives
(30 30 45 50 | 100 )
(30 27 15 18 | 90 )
taking second minus the first row and then dividing the first one by 5
to go back gives
(6 6 9 10 | 20 )
(0 -3 -30 -32 |-10 )
adding twice the second row to the first row gives
(6 0 -51 -54 | 0 )
(0 -3 -30 -32 | -10)
So s = (51/6) a + 9p
d = 10/3-10a - (32/3)p
and a and p are arbitrary. So, for example, setting a = p = 0 gives s
= 0, d = 10/3, which is a solution to the original system.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@math.berkeley.edu |
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Dave Rusin
science forum Guru
Joined: 25 Mar 2005
Posts: 487
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| Posted: Wed May 04, 2005 1:34 am Post subject:
Re: Need Help Solving FOUR Unknowns
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In article <1115155333.076605.109190@g14g2000cwa.googlegroups.com>,
Jojo Manzo <jojomanzo@gmail.com> wrote:
| Quote: | I have THREE problems, with FOUR unknowns in each, is there any way I
can solve them , I assume I may get more than one set of possible
answers, can anyone help?
6s + 6d + 9a + 10p = 20
10s + 9d + 5a + 6p = 30
16s + 15d + 14a + 16p = 50
|
Did these equations arise in an application? Is it important that
the solutions s,d,a,p be integers? Is it important that they be
positive? Is there a reason to prefer one solution over another?
Those kinds of questions can really change the kind of answer you
will get when you say "need help solving".
dave |
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