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Math Help - Combining equations

  1. #1
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    Combining equations

    Hi,
    I have two equations that I need to combine to find the value of a variable. My tutor has been through this but I don't get it. Please could you walk me through the steps?

    I have 1)Vr = Vm/FCR and 2)VL = Vm-Vr/2 and I need to solve for Vm by substituting equation 1 into equation 2.

    The answer I have is Vm=VL/(1-(1/ 2FCR) but I want to know how to get there.
    Thanks for your time
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  2. #2
    Senior Member sakonpure6's Avatar
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    Re: Combining equations

    Which variable, Vr, Vm, Vl? From your concluded answer I assume it is Vr?
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  3. #3
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    Re: Combining equations

    Quote Originally Posted by Daveinthebigcity View Post
    Hi,
    I have two equations that I need to combine to find the value of a variable. My tutor has been through this but I don't get it. Please could you walk me through the steps?

    I have 1)Vr = Vm/FCR and 2)VL = Vm-Vr/2 and I need to solve for Vm by substituting equation 1 into equation 2.

    The answer I have is Vm=VL/(1-(1/ 2FCR) but I want to know how to get there.
    Thanks for your time
    Start with equation 1

    V_r=\frac{V_m}{FCR}

    now substitute this into equation 2

    V_L=V_m-\frac{V_r}{2}

    V_L=V_m-\frac{\frac{V_m}{FCR}}{2}=V_m-\frac{V_m}{2FCR}=V_m\left(1-\frac{1}{2FCR}\right)

    so

    V_m=\frac{V_L}{\left(1-\frac{1}{2FCR}\right)}

    Clear?
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  4. #4
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    Re: Combining equations

    Hi,
    That has helped me a lot. I see where I went wrong now. Much obliged :-)
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