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#1 2010-01-31 07:31:22
- Shiiro
- Member
- Registered: 2009-11-30
- Posts: 27
Solve The System
Hi ,
Solve the system following in
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#2 2010-01-31 11:01:54
- Shiiro
- Member
- Registered: 2009-11-30
- Posts: 27
Re: Solve The System
Can You Help me ??
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#3 2010-01-31 12:54:06
- Ricky
- Moderator
- Registered: 2005-12-04
- Posts: 3,791
Re: Solve The System
Do you need all solutions? There is an obvious one you can see.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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#4 2010-01-31 13:13:07
- Shiiro
- Member
- Registered: 2009-11-30
- Posts: 27
Re: Solve The System
Yes I need all solutions plz !
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#5 2010-01-31 14:30:50
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Solve The System
Hi Shiiro;
From a computer search:
z = 0 there are only 2 solutions that I can find.
z = 1 there are an infinite number of solutions
z = 2 there are no solutions that I can find.
z = 3 there are only 2 solutions that I can find.
z = 4 there are no solutions that I can find.
z = 5 there are no solutions that I can find.
z = 6 there are only 2 solutions that I can find.
For 6 < z < 0 I can find no solutions.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#6 2010-01-31 15:14:04
- Ricky
- Moderator
- Registered: 2005-12-04
- Posts: 3,791
Re: Solve The System
Substitute x = 1-y-z into the 2nd equation, and you get
This gives the infinitely many solutions for z=1, and y can be chosen arbitrarily with x = 1-y-z. It also proves that if z is not 1, then 3 must divide z.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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#7 2010-01-31 15:16:42
- Ricky
- Moderator
- Registered: 2005-12-04
- Posts: 3,791
Re: Solve The System
When divided by 3, y can not leave a remainder of 2.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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#8 2010-01-31 15:22:53
- Ricky
- Moderator
- Registered: 2005-12-04
- Posts: 3,791
Re: Solve The System
y must be in the set {-3, -2, -1, 0, 1}
It should be easy from here. To come up with this restriction, use my previous post #6.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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