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Math Help - Solving system of equations

  1. #1
    Super Member Deadstar's Avatar
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    Solving system of equations

    Find the general integer solution (x, y, z) to the pair of equations

    3x + 4y + 7z = 1
    5x + 9y + 2z = 3

    Put t = x + y + 2z. Then we have;
    3t + y + z = 1
    5t + 4y - 8z = 3:
    Eliminating y, we get 7t + 12z = 1.

    I can't solve this last part. I don't know why, it should be so easy... It should be...
    (t, z) = (-5 + 12u, 3 - 7u), u an arbitrary integer but I'm nowhere near that. I end up doing about 4 substitutions but it all goes in a mess.
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  2. #2
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    Why not just parameterize with your free variable z, and use it to describe x and y, instead of introducing t, u and everything else?
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  3. #3
    Super Member Deadstar's Avatar
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    Damn I'm gonna need to put in a lot of pre done stuff so this makes sense them...

    This is previous questions which I have done and solved but just taken straight from the questions and answers.

    First pic is solving one linear equation, 2nd slide is the solution.

    3rd pic is solving a linear system.
    Attached Thumbnails Attached Thumbnails Solving system of equations-untitled.jpg   Solving system of equations-untitled1.jpg   Solving system of equations-untitled2.jpg  
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  4. #4
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    do you have to solve it with that method? I know there are teachers that want it solved with a particular method sometimes, so is that the case here? if not, why not solve it another way?
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  5. #5
    Super Member Deadstar's Avatar
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    Yes that's the method we have to use.

    I have done a few of them, it's really quite a simple thing once you get the hang of it but I just can't get this one done...

    Here's an example of a linear equation (not a system), to show you what's going on. (in attachment)

    This is using the question from the first slide in my previous post.
    Attached Thumbnails Attached Thumbnails Solving system of equations-untitled.jpg  
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