# How to find the intersection point of four equations?

Posted 7 months 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. The equations are in terms of the four variables. Can you please tell me how to find the intersection? Y2 =.; Y3 =.; l2 =.; l3 =.; Y1 = 0.0125; l1 = 0.0108366; lambda = {0.043656,0.0410959,0.0413712,0.0433463,0.0423413}; b1 = 0.0502519; b3 = 0.0161692; 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 7 months ago
 The code doesn't work for me ?
Posted 7 months 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.
Posted 7 months ago
 There are several undefined symbols in the code, t11, t21, t13 ....
Posted 7 months ago
Posted 7 months ago
 The code doesn't work for me, with fresh kernel? Update the code.What is that:  Y2 =.; ?
Posted 7 months ago
 Hi Mariusz,=. is syntax for Unset.
Posted 7 months ago
 I defined it as a variable.
Posted 7 months ago
 t11 is still missing.
Posted 7 months ago
 Sorry. Updated the code.
Posted 7 months ago
 There are still undefined symbols. Execute the latest code against a new kernel.
Posted 7 months 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.