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Math Help - solving simultaneous equations

  1. #1
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    Exclamation solving simultaneous equations

    Hi, I'm doing electrical systems and I have an issue with solving the simultaneous equations after nodal analysis. can someone please show me the steps, I know it's basic, but I'm pretty desperate.

    (-2)((V1-Vth)/80)+((Vth-V1)/20)=0

    ((V1-24)/20)+((V1-Vth)/20)+((V1-4Vth)/80)=0


    any help will be great thanks.
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  2. #2
    MHF Contributor
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    Re: solving simultaneous equations

    In this case, I'm tempted to multiply the world by 80.

    [-2 * (V1 - Vth)] + [4 * (Vth - V1)] = 0

    [4 * (V1 - 24)] + [4 * (V1 - Vth)] + [(V1 - 4Vth)] = 0

    SO much nicer. Okay, now what?
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  3. #3
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    Re: solving simultaneous equations

    ok, do I multiply it out or can I take a common factor of 2 out of the first one? (I told you I really needed help :P)
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: solving simultaneous equations

    You can reform the first equation to:
    -2(v_1-v_{th})+4(v_{th}-v_1)=0 \Leftrightarrow -2(v_1-v_{th})=-4(v_{th}-v_1) \Leftrightarrow v_1-v_{th}=2(v_{th}-v_1)\Leftrightarrow v_1-v_{th}=2v_{th}-2v_1
    \Leftrightarrow v_1+2v_1=2v_{th}+v_{th} \Leftrightarrow v_1=v_{th}

    So if you use this substitution in the second equation then you have a first degree equation in one variable.
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