How can I solve this complex 4 equation with 4 unknowns

Hello,

I am having a very hard time solving for the following 4 equations with 4 unknonws.

269.0 = R1*(R2+R3+R4)/(R1+R2+R3+R4)

267.8 = R2*(R1+R3+R4)/(R1+R2+R3+R4)

265.8 = R3*(R1+R2+R4)/(R1+R2+R3+R4)

267.3 = R4*(R1+R2+R3)/(R1+R2+R3+R4)

I was able to narrow it down to:

R4=267.3(R1+R2+R3)/(R1+R2+R3-267.3)

R3=265.8(R1+R2+R4)/(R1+R2+R4-265.8)

R2=267.8(R1+R3+R4)/(R1+R3+R4-267.8)

R1=269.0(R2+R3+R4)/(R2+R3+R4-269.0)

How do I solve for R1 R2 R3 and R4 using matlab? I tried the following code but I don't think it's giving me the right answer:

[R1,R2,R3,R4]=solve('R1=269.0(R2+R3+R4)/(R2+R3+R4-269.0)','R2=267.8(R1+R3+R4)/(R1+R3+R4-267.8)','R3=265.8(R1+R2+R4)/(R1+R2+R4-265.8)','R4=267.3(R1+R2+R3)/(R1+R2+R3-267.3)','R1','R2','R3','R4')

Answer 1

[Azzi Abdelmalek]

equ1='269.0-R1*(R2+R3+R4)/(R1+R2+R3+R4)'
equ2='267.8-R2*(R1+R3+R4)/(R1+R2+R3+R4)'
equ3='265.8- R3*(R1+R2+R4)/(R1+R2+R3+R4)'
equ4='267.3 - R4*(R1+R2+R3)/(R1+R2+R3+R4)'
sol=solve(equ1,equ2,equ3,equ4)

[Thamer]

Thank you Azzi for your response.

I pasted your code into Matlab and here is what I got:

sol = 

      R1: [4x1 sym]
      R2: [4x1 sym]
      R3: [4x1 sym]
      R4: [4x1 sym]

What does this answer mean? I don't see any values for R1 R2 R3 R4.

Thank you

[Azzi Abdelmalek]

R1=sol.R1
R2=sol.R2
R3=sol.R3
R4=sol.R4

[Thamer]

Once again, thank you Azzi! I am now able to get the values for the resistors.

[Thamer]

One last question Azzi, Is there a way to tell Matlab to give me only the positive answer in the R matrices? (since in real life R cannot be negative)

[Walter Roberson]

syms R1 R2 R3 R4 positive
equ1=269.0-R1*(R2+R3+R4)/(R1+R2+R3+R4);
equ2=267.8-R2*(R1+R3+R4)/(R1+R2+R3+R4);
equ3=265.8- R3*(R1+R2+R4)/(R1+R2+R3+R4);
equ4=267.3 - R4*(R1+R2+R3)/(R1+R2+R3+R4);
sol=solve(equ1,equ2,equ3,equ4)

[Azzi Abdelmalek]

Or

equ1='269.0-R1*(R2+R3+R4)/(R1+R2+R3+R4)'
equ2='267.8-R2*(R1+R3+R4)/(R1+R2+R3+R4)'
equ3='265.8- R3*(R1+R2+R4)/(R1+R2+R3+R4)'
equ4='267.3 - R4*(R1+R2+R3)/(R1+R2+R3+R4)'
sol=solve(equ1,equ2,equ3,equ4,'R1>0','R2>0','R3>0','R4>0')

[Thamer]

Thank you guys, both method worked. I appreciate all the help.

Answer 2

[Walter Roberson]

R1 = -.1528124199, R2 = .1523845305, R3 = -.1519010380, R4 = .1522421676

R1 = 1.350702113, R2 = -1.354494804, R3 = -1.349440249, R4 = 1.346416572

R1 = 359.6939654, R2 = 357.2814545, R3 = 353.2965306, R4 = 356.2810534

R1 = 1.849064292, R2 = 1.844921136, R3 = -1.850793347, R4 = -1.855990235

Any imaginary components are vanishingly small and only appear due to round-off error.

[Thamer]

Thank you for replying Walter. Using Azzi's matlab code above I managed to get the same answers as yours.

And since R's cannot be negative, the only possible solution would be: R1 = 359.6939654, R2 = 357.2814545, R3 = 353.2965306, R4 = 356.2810534

Have a good rest of the week!