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Math Help - Can't solve system

  1. #1
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    Jan 2010
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    Can't solve system


    Find the general solution of the following system. Indicate which variables are basic and which
    are free.

    -2x1 + 3x2 + 3x3 + 2x4 = -9
    3
    x1 - 4x2 + x3 = 5

    -
    5x1 + 7x2 + 2x3 -3/2x4 = -14


    The answer that i got is wrong( Can anyone could help me to solve this please?
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  2. #2
    MHF Contributor
    Joined
    Dec 2009
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    Thanks
    1
    If you subtract line2 from line1 you get line3.

    -2x_1+3x_2+3x_3+2x_4-(3x_1-4x_2+x_3)=5x_1+7x_2+2x_3-\frac{3}{2}x_4

    -5x_1+7x_2+2x_3+2x_4=5x_1+7x_2+2x_3-\frac{3}{2}x_4

    2x_4-5x_1=5x_1-\frac{3}{2}x_4

    \frac{7}{2}x_4=10x_1

    x_4=\frac{20}{7}x_1

    -2x_1+3x_2+3x_3+\frac{40}{7}x_1=\frac{26}{7}x_1+3x_  2+3x_3=-9

    3x_1-4x_2+x_3=5

    5x_1+7x_2+2x_3-\frac{30}{7}x_1=\frac{5}{7}x_1+7x_2+2x_3=-14

    This is now 3 simultaneous equations in 3 unknowns,
    which can now be solved in the usual way.
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