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}]
