# How to find the intersection point of four equations?

Posted 10 days ago
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 Hi, I have four equations of four variables. I defined the range of the four variables and I need to find the intersection of the four equations in the given range. Y2 =.; Y3 =.; l2 =.; l3 =.; Y1 = 0.02; l1 = 0.0105698; lambda = {0.0426, 0.0401, 0.0403, 0.0423, 0.0413}; b1 = 0.0804031; b3 = 0.0258706; t21 = ((2*Pi)/lambda[[1]])*l2; t31 = ((2*Pi)/lambda[[1]])*l3; t23 = ((2*Pi)/lambda[[5]])*l2; t33 = ((2*Pi)/lambda[[5]])*l3; t11 = ((2*Pi)/lambda[[1]])*l1; t13 = ((2*Pi)/lambda[[5]])*l1; Manipulate[t21 = (2*Pi/lambda[[1]])*l2; t31 = (2*Pi/lambda[[1]])*l3; t23 = (2*Pi/lambda[[5]])*l2; t33 = (2*Pi/lambda[[5]])*l3; plot = Plot[{2*Y1*Tan[t11] + Y2*Tan[t21] + Y3*Tan[t31], 2*Y1*Tan[t13] + Y2*Tan[t23] + Y3*Tan[t33], t11*Y1 + t21*(Y2/2)*(Sec[t21]^2/Sec[t11]^2) + t31*(Y3/2)*(Sec[t31]^2/Sec[t11]^2) - b1, t13*Y1 + t23*(Y2/2)*(Sec[t23]^2/Sec[t13]^2) + t33*(Y3/2)*(Sec[t33]^2/Sec[t13]^2) - b3}, {Y3, 0.008, 0.05}], {Y2, 0.008, 0.05}, {l3, 0.008, 0.012}, {l2, 0.008, 0.012}] 
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Posted 10 days ago
 The code doesn't work for me ?
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Posted 10 days ago
 The range can be increased by {Y9,0.008,0.05}, {Y2,0.008,0.05},{l33,0.008,0.012},{l22,0.008,0.012}. Any problem with the code? Its working fine for me. Please let me know.
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Posted 10 days ago
 There are several undefined symbols in the code, t11, t21, t13 ....
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Posted 10 days ago
 Please check the edited code.
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Posted 10 days ago
 The code doesn't work for me, with fresh kernel? Update the code.What is that:  Y2 =.; ?
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Posted 10 days ago
 Hi Mariusz,=. is syntax for Unset.
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Posted 10 days ago
 I defined it as a variable.
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Posted 10 days ago
 t11 is still missing.
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Posted 10 days ago
 Sorry. Updated the code.
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Posted 10 days ago
 There are still undefined symbols. Execute the latest code against a new kernel.
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Posted 9 days ago
 Please check the updated code.
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Posted 9 days ago
 Why do you believe there is a simultaneous zero in those ranges of the variables? FindRoot and FindMinimum fail to locate any zero. And the Manipulate does not indicate likelihood of such either, as best I can tell.
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Posted 8 days ago
 It'll not be an exact zero but its a very small value of the order of 10^(-29). I need to find the values of the 4 unknowns from the plot. I guess the solution gets trapped in local minima.
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