Three Unknown Resistances: Solving for Unknowns in a System of Equations

[flash]

I need to find three unknown resistances given the following three equations:

$$\frac{1}{R_2+R_3} + \frac{1}{R_1} = \frac{1}{670}$$

$$\frac{1}{R_1+R_3} + \frac{1}{R_2} = \frac{1}{679}$$

$$\frac{1}{R_1+R_2} + \frac{1}{R_3} = \frac{1}{1349}$$

I figured since there are three unknowns and three equations it is possible, but I can't see how its done.

 

[Sleek]

Sorry, I'm in a slight hurry, but it may be done in this way,

If you take LCM in all the three equations, you find that the numerator of the LHS becomes equal. If the denominators are take to the RHS, you'll get something like

$$\displaystyle \frac{R_1(R_2+R_3)}{670}=\frac{R_2(R_1+R_3)}{679}=\frac{R_3(R_1+R_2)}{1349}$$

The above equation might help as it is much simpler. Maybe you can try solving the above.

Regards,
Sleek

 

[flash]

Wow, thanks heaps. Took me a while to figure out how you got that :) It should be a lot easier now.