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Math Help - Simultaneous Equations

  1. #1
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    Simultaneous Equations

    Through using substitution how can I solve

    3p-3 = q
    and
    7p=1+4q

    so that p=-1 and q=-2

    I am really interested in the working out, the how and the why. If that makes sense.

    Many Thanks in advance
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Simultaneous Equations

    Substitute the first equation (q=...) in the second equation therefore you get a first degree equation in p.
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  3. #3
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    Re: Simultaneous Equations

    Thats the problem I have rewritten the first equation so that p = 3q+3/3 and tried to substitute it into 7p = 1 + 4q but I am getting nowhere.
    Any hints would be appreciated
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Simultaneous Equations

    Yes, but you see the first equation is q=..., so you can directly substitute q=3p-3 in the second one therefore you get:
    7p=1+4(3p-3)
    Solve this equation for p, afterwards you can find q
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  5. #5
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    Re: Simultaneous Equations

    Quote Originally Posted by planetdomi View Post
    Through using substitution how can I solve

    3p-3 = q
    and
    7p=1+4q

    so that p=-1 and q=-2

    I am really interested in the working out, the how and the why. If that makes sense.

    Many Thanks in advance
    So sorry I go the equations wrong

    3p-3 = 3q

    and

    7p = 1 + 4q
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Simultaneous Equations

    No problem, it's just the same way. If you divide in the first equation every side by 3 then you get p-1=q, now substitute this in the second equation therefore the equation becomes:
    7p=1+4(p-1)

    What do you get for p? And q?
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  7. #7
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    Re: Simultaneous Equations

    Feel like a fool for not getting it
    Makes perfect sense now

    thanks
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  8. #8
    MHF Contributor Siron's Avatar
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    Re: Simultaneous Equations

    Quote Originally Posted by planetdomi View Post
    Feel like a fool for not getting it
    Makes perfect sense now

    thanks
    You're welcome! You don't have to feel like a fool, everyone has to learn, but it's important to exercice a lot.
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