# Combining equations

#### Daveinthebigcity

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.

#### sakonpure6

Which variable, Vr, Vm, Vl? From your concluded answer I assume it is Vr?

#### romsek

MHF Helper
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.

$$\displaystyle V_r=\frac{V_m}{FCR}$$

now substitute this into equation 2

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

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

so

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

Clear?

#### Daveinthebigcity

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