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Math Help - basic unknowns in a system

  1. #1
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    basic unknowns in a system

    My text says that the system


    5x+y=3

    4x_1-x_2+3x_3=-1

    has unknowns x and y

    I would have thought it has more than just x and y.

    This is the full excerpt.

    basic unknowns in a system-picture-48.png
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: basic unknowns in a system

    i'm pretty sure they messed up the ordering Like

    (5) is supposed to be 5x+y = 3 , 2x-y = 4
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  3. #3
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    Re: basic unknowns in a system

    It looks to me like they are just numbered wrong. That is "system 5" refers to the two equations on the left, 5x+ y= 3 and 2x- y=4, while "system 6" refers to the two equations on the right 4x_1- x_2+ 3x_3= -1 and 3x_1+ x_2+ 9x_3= -4.

    The first system, two equations in two unknowns, has the unique solution x= 1, y= -2: 5(1)- 2= 3, 2(1)-(-2)= 4.

    The second system, two equations in three unknowns, has an infinite number of solutions.
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  4. #4
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    Re: basic unknowns in a system

    That's what I thought might be the case. Thanks!
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