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    DOAalex's Avatar
    DOAalex Posts: 2, Reputation: 1
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    #1

    Mar 4, 2010, 07:53 PM
    How do you solve 3x 7y=-1 2x+3y=6 in the substitution method
    I have tried the addition method on this problem where I multiple both equations if the constant but my teacher swears there is another better way so please help me
    ROLCAM's Avatar
    ROLCAM Posts: 1,420, Reputation: 23
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    #2

    Mar 4, 2010, 08:30 PM

    3x + 7y= -1
    2x + 3y= 6
    _______________
    6X + 14Y = -2
    -6X - 9Y = -18
    ________________

    5Y = -20
    Y = -4
    ________________
    2x + 3y = 6
    2X -12 = 6
    2X = 6+12
    2X = 18
    X =9

    _______________________

    X=9
    Y = -4
    ___________________________
    proof:-

    3x + 7y= -1 ****27-28 = -1
    2x + 3y= 6 *****18-12 = 6
    KISS's Avatar
    KISS Posts: 12,510, Reputation: 839
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    #3

    Mar 4, 2010, 09:32 PM

    You need to solve one of the equations for x or y and substitute into the other one. It will be a little messy. Fractions.
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #4

    Mar 5, 2010, 12:44 PM

    Well, strictly speaking, yes, using substitution will give rise to fractions, making it a little messy.

    You can try substituting something else instead of x or y to make is easier.

    3x + 7y= -1
    2x + 3y= 6

    Multiply (I) by 2 and (ii) by 3.

    6x + 14y= -2
    6x + 9y= 24

    Make 6x the subject of formula in the first equation.

    6x = -2 - 14y

    Now, substitute 6x by (-2 -14y) into the other equation, giving:

    (-2 - 14y) + 9y= 24

    You substituted 6x instead of x. Now it's easier.
    KISS's Avatar
    KISS Posts: 12,510, Reputation: 839
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    #5

    Mar 5, 2010, 01:59 PM

    Why didn't I think of that? (Can't spread rep).
    Unknown008's Avatar
    Unknown008 Posts: 8,076, Reputation: 723
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    #6

    Mar 6, 2010, 08:21 AM

    Don't worry :) This happens to me as well.
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