# Solving two nonlinear equations

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Franziska on 7 May 2019
Commented: Franziska on 21 May 2019
I want to solve two non-linear equations of the variables and in terms of the third variable A:
where and given. I need and as a function of A only (given α), such that I can plot the solution over a range of A between 0.5 and 2.
I tried to solve the system symbolically, but did not find a solution.
Any Ideas?

Torsten on 7 May 2019
Edited: Torsten on 7 May 2019
A = 0.5:0.01:2;
alpha = 0.5;
l00 = 1;
for i = 1:numel(A)
a = A(i);
fun = @(l0) 1 + alpha*l0^(alpha-1) - l0 - alpha*a*(2-l0)^(alpha-1);
L0(i) = fzero(fun,l00);
L1(i) = 2 - L0(i);
l00 = L0(i);
end
plot(A,L0,A,L1)
%res_L0 = 1-alpha*A.*L1.^(alpha-1)+alpha*L0.^(alpha-1)-L0;
%res_L1 = 1+alpha*A.*L1.^(alpha-1)-alpha*L0.^(alpha-1)-L1;
%plot(A,res_L0,A,res_L1)
Franziska on 7 May 2019
thanks it works!
Franziska on 21 May 2019
Is there any way to get the actual functions and as a function of A?
Such that is a function of A only, and is a function of A only?