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Math Help - Systems if linear equations

  1. #1
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    Systems if linear equations

    I am lost as to how to find the solution to this equation:
    x - 2z =1
    y + z = 3

    Correct answer:
    x = 1 + 2r
    y = 3 - r
    z = r

    Where did this r come from?! Why is it being used?
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  2. #2
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    Quote Originally Posted by rizzod206 View Post
    I am lost as to how to find the solution to this equation:
    x - 2z =1
    y + z = 3

    Correct answer:
    x = 1 + 2r
    y = 3 - r
    z = r

    Where did this r come from?! Why is it being used?
    r is called a parameter, you have 3 unknowns and 2 equations which if you recall from high school algebra, means you do not have enough info to find a solution

    when we say z=r and y=3-r and x=1+2r what this really means is you have enough info to determine y=3-z and x=1+2z, but because we lack a 3rd equation you can let z be anything

    So particular solutions are of the form (1+2r,3-r,r) where you pick some number for r and then plug it in
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