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 Post subject: Equation solvePosted: Fri, 9 Dec 2011 10:14:33 UTC
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Joined: Fri, 9 Dec 2011 09:50:22 UTC
Posts: 1
How can I solve linear equations which have more variables than its equation for example how can I solve this

x+y+z=9

4x+8y+6z=23

Here three variable but two equation.Please tell me the procedure of solving such equation.

Thank you

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 Post subject: Re: Equation solvePosted: Fri, 9 Dec 2011 10:50:15 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6007
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Moved from Applied to Matrix Algebra.

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 Post subject: Re: Equation solvePosted: Fri, 9 Dec 2011 10:54:48 UTC
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shamim2k8 wrote:
How can I solve linear equations which have more variables than its equation for example how can I solve this

x+y+z=9

4x+8y+6z=23

Here three variable but two equation.Please tell me the procedure of solving such equation.

Thank you

Start by finding a particular solution. Then find the kernel of

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 Post subject: Re: Equation solvePosted: Fri, 9 Dec 2011 14:48:42 UTC
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Joined: Mon, 19 May 2003 19:55:19 UTC
Posts: 7949
Location: Lexington, MA
Hello, shamim2k8!

Quote:
How can I solve linear equations which have more variables than equations?

. .

We will have an infinite number of solutions.
. . We must find a neat way to say this.

Eliminate a variable, say,

And we have: .

. . Solve for

Substitute into [1]: .

. . Solve for

We have: .

On the right, replace with a parameter

. . And we have: .

We have a solution for every real number

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 Post subject: Re: Equation solvePosted: Fri, 9 Dec 2011 21:06:48 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12102
Location: Austin, TX
For completeness it should be stated that you are not guaranteed infinitely many solutions in general. For the system:

there are NO solutions, so just be careful of that.

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