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Math Help - Linear equations with letter variables

  1. #1
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    Linear equations with letter variables

    Hey everyone, I have 4 questions which I know is a lot to ask but would really appreciate the answers to. Just open the link and click to zoom.
    Thanks!

    http://img251.yfrog.com/img251/56/15671906.png
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  2. #2
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    17. The system is consistent as long as the equations are not scalar multiples of each other.

    Notice that the first row:

    2x + 3y = h

    is the same as

    4x + 6y = 2h.


    So we can not let 2h = 7.

    What value of h can we not have?

    Then what values of h can we have?
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  3. #3
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    18.

    Equation 1 is

    x - 3y = -2

    which is the same as

    5x - 15y = -10.

    The two equations are not scalar multiples of each other, so you can have h be whatever you like.
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  4. #4
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    Quote Originally Posted by Prove It View Post
    17. The system is consistent as long as the equations are not scalar multiples of each other.
    That's not exactly true. The system is consistent as long as no equation is a linear combination of the others- that may be what you meant by "scalar multiples". Certainly, if one is a multiple of another, that is a "linear combination". so it works for this problem.

    Notice that the first row:

    2x + 3y = h

    is the same as

    4x + 6y = 2h.


    So we can not let 2h = 7.

    What value of h can we not have?

    Then what values of h can we have?
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