4 equations, 4 unknowns

[malsch]

First of all hi,

I was working some mathematics and ended up with 4 unknowns with 4 equations. I tried substituting equations but ended up with squared unknowns as shown in the following picture:

**broken link removed**

Any help on how to solve this would be greatly appreciated.

Thank you.

 

[misterT]

Do you want an example of how to solve that thing or just the answer? Here are the answers:

L = -0.0127604
C = -2.19085*10^-6
G = -0.000145066
R = -7.508

Or

L = 0.0127604
C = 2.19085*10^-6
G = 0.000145066
R = 7.508

There are also 2 imaginary answers:

L = 0 - 0.0238971 i
C = 0 - 4.61822*10^-7 i
G = 0 + 0.000688312 i
R = 0 + 4.00869 i

OR

L = 0 + 0.0238971 i
C = 0 + 4.61822*10^-7 i
G = 0 - 0.000688312 i
R = 0 - 4.00869 i

 

[malsch]

Hi misterT,

the following answers do make sense to the rest of my question:

L = 0.0127604
C = 2.19085*10^-6
G = 0.000145066
R = 7.508

I was wondering what method you used to conclude to them...

Thank you

 

[misterT]

I used Wolfram Mathematica to solve the problem numerically.. Just wanted to provide you with an answer. I don't have time to work it out on paper (at least for now).

You could try a technique called Completing the square if you want to solve it by hand (to the equations 5 and 6).