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Math Help - Linear equality system with 5 variables

  1. #1
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    Linear equality system with 5 variables

    So here is the system:

    V+W+X+Y+Z=7
    X+2y+3z=8
    x+2y+5z=10

    I used Gaussian elimination method and got this:

    V+W+X+Y+Z=7
    X+2Y+3Z=8
    -2Z=-2

    So from here I can get z=1 but couldn't go up from here as the next equation (x+2y+3z)=8 has two other unknowns and the other is even worse with 5 variables. Anyone help please?
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  2. #2
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    Quote Originally Posted by Keep View Post
    So here is the system:

    V+W+X+Y+Z=7
    X+2y+3z=8
    x+2y+5z=10

    I used Gaussian elimination method and got this:

    V+W+X+Y+Z=7
    X+2Y+3Z=8
    -2Z=-2

    So from here I can get z=1 but couldn't go up from here....
    You have five variables but only three equations. Where, "from here", were you needing to "go"? (Such systems cannot typically be solved for a unique solution.)
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  3. #3
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    Quote Originally Posted by stapel View Post
    You have five variables but only three equations. Where, "from here", were you needing to "go"? (Such systems cannot typically be solved for a unique solution.)
    I was just wondering if there was a way I can find a solution to the variables even if it is something like 0=2 which means the system is unsolvable etc. So it is not possible to do anything beyond the point of getting the value of z as 1? So I just leave it that way and write 'system unsolvable?'
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  4. #4
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    The system may be solveable. It's just not uniquely solveable. It's like a "system" of one equation in two variables: All you can do is solve "in terms of" the extra variables. You cannot find unique numerical solutions.
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  5. #5
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    Quote Originally Posted by stapel View Post
    The system may be solveable. It's just not uniquely solveable. It's like a "system" of one equation in two variables: All you can do is solve "in terms of" the extra variables. You cannot find unique numerical solutions.
    Is it possible to do that then since that is what I want i.e. solving for the extra variables such that I can find the values of v,w,x,y,z or until I get some nonsense result like 0=3 etc thereby 'proving' it is not a uniquely solvable system?
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