MATLAB: 11 equations with 2 unknowns

multiple equationssolve

I'm trying to find the constant in these 11 eqns using solver. But after I run the file, it shows:"Empty sym: 0-by-1". Any help is appreciated here. Thank you.
Here's the command I wrote:
Pultem = 1.48; %Pc
PPIM1 = 3488.7; %Pd
lambda = PPIM1/Pultem;
syms a b
E1 = ((a*(b-0)+(a+b*0)*lambda)/((a+0)+(b-0)*lambda) - 1.48)==0;
E2 = ((a*(b-0.055)+(a+b*0.055)*lambda)/((a+0.055)+(b-0.055)*lambda) -2.18)==0;
E3 = ((a*(b-0.109)+(a+b*0.109)*lambda)/((a+0.109)+(b-0.109)*lambda) -3.95)==0;
E4 = ((a*(b-0.217)+(a+b*0.217)*lambda)/((a+0.217)+(b-0.217)*lambda) -6.58)==0;
E5 = ((a*(b-0.322)+(a+b*0.322)*lambda)/((a+0.322)+(b-0.322)*lambda) -9.27)==0;
E6 = ((a*(b-0.526)+(a+b*0.526)*lambda)/((a+0.526)+(b-0.526)*lambda) -51.7)==0;
E7 = ((a*(b-0.773)+(a+b*0.773)*lambda)/((a+0.773)+(b-0.773)*lambda) -477.1)==0;
E8 = ((a*(b-0.817)+(a+b*0.817)*lambda)/((a+0.817)+(b-0.817)*lambda) -1259.7)==0;
E9 = ((a*(b-0.909)+(a+b*0.909)*lambda)/((a+0.909)+(b-0.909)*lambda) -2876.6)==0;
E10 = ((a*(b-0.955)+(a+b*0.955)*lambda)/((a+0.955)+(b-0.955)*lambda) -3275.9)==0;
E11 = ((a*(b-1)+(a+b*1)*lambda)/((a+1)+(b-1)*lambda) -3488.7)==0;
vars = [a b];
[sola, solb]= vpasolve(E1,E2,E3,E4,E5,E6,E7,E8,E9,E10,E11,vars);
>> sola
sola =
Empty sym: 0-by-1

Best Answer

The system is overdetermined, therefore, it is highly unlikely that it will have a unique solution. The best you can expect is a least square solution. You can refer to answer here to see how can you use fmincon() to obtain a least square solution. The general idea is to make an objective function like this
objfun = E1^2 + E^2 + E^3 + ..... + E11^2
and minimize it using fmincon() for a and b.
Edit:
You code will become
Pultem = 1.48; % Pc 
PPIM1 = 3488.7; %Pd
lambda = PPIM1/Pultem;
syms a b
E(1) = ((a*(b-0)+(a+b*0)*lambda)/((a+0)+(b-0)*lambda) - 1.48);
E(2) = ((a*(b-0.055)+(a+b*0.055)*lambda)/((a+0.055)+(b-0.055)*lambda) -2.18);
E(3) = ((a*(b-0.109)+(a+b*0.109)*lambda)/((a+0.109)+(b-0.109)*lambda) -3.95);
E(4) = ((a*(b-0.217)+(a+b*0.217)*lambda)/((a+0.217)+(b-0.217)*lambda) -6.58);
E(5) = ((a*(b-0.322)+(a+b*0.322)*lambda)/((a+0.322)+(b-0.322)*lambda) -9.27);
E(6) = ((a*(b-0.526)+(a+b*0.526)*lambda)/((a+0.526)+(b-0.526)*lambda) -51.7);
E(7) = ((a*(b-0.773)+(a+b*0.773)*lambda)/((a+0.773)+(b-0.773)*lambda) -477.1);
E(8) = ((a*(b-0.817)+(a+b*0.817)*lambda)/((a+0.817)+(b-0.817)*lambda) -1259.7);
E(9) = ((a*(b-0.909)+(a+b*0.909)*lambda)/((a+0.909)+(b-0.909)*lambda) -2876.6);
E(10) = ((a*(b-0.955)+(a+b*0.955)*lambda)/((a+0.955)+(b-0.955)*lambda) -3275.9);
E(11) = ((a*(b-1)+(a+b*1)*lambda)/((a+1)+(b-1)*lambda) -3488.7);
Ehandle = matlabFunction(sum(E.^2));
sol = fmincon(@(x) Ehandle(x(1), x(2)),[1 1], [], []);
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