Solving a system of nonlinear equations

I have a system of equation like this, and I want to find x1 and x2 with different value of C (from 1 to 10). What functions and commands should I use?

I tried something like this , but it is taking forever to run.

syms x y c

K1=1.930*10^-4;
K2=5.528;
k = 0:1/100:1
 eq =((x -y)/(10+2*x)*((3*x+y)/(10+2*x))^3)/((c-x)/(10+2*x)*(10-c-x-y)/(10+2*x)==K1);
 eq2 = (y/(10+2*(x))*(3*(x)+y)/(10+2*x))/(x-y/(10+2*x)*((10-c-x-y)/(10+2*x))==K2);
vars = [x y];
[solx,soly]= vpasolve([(subs(eq,c,k)),subs(eq2,c,k)],vars,true)

Answer 1

[Sulaymon Eshkabilov]

Hi,

Here is the solution to your problem in which C is taken to have values C = 1:10 that can have any values.

clearvars; clc
syms x y 
K1=1.930*10^-4;
K2=5.528;
C = 1:10;
for ii=1:numel(C)
 eq1 =((x -y)/(10+2*x)*((3*x+y)/(10+2*x))^3)/((C(ii)-x)/(10+2*x)*(10-C(ii)-x-y)/(10+2*x)==K1);
 eq2 = (y/(10+2*(x))*(3*(x)+y)/(10+2*x))/(x-y/(10+2*x)*((10-C(ii)-x-y)/(10+2*x))==K2);
xy = solve(eq1, eq2);
X_sol(ii, :) = double(xy.x);
Y_sol(ii, :) = double(xy.y);
end

% Note the solutions of x and y are X_sol and Y_sol. Some of their values are complex.

Good luck.

[madhan ravi]

Why is k defined ? , never seemed to be used anywhere.

[madhan ravi]

Sulaymon Eshkabilov‘S answer moved here:

I don't see k in your equation. Indeed, k is not needed at all ... in my code.

[madhan ravi]

Well, see the fifth line in your code. By the way, there’s no need to keep adding answer to make a comment, use comment on this answer .

[Walter Roberson]

Be careful here. MATLAB is able to find 11 solutions for symbolic c, each with a condition under which it is true. The conditions are not necessarily all consistently true in the range 1 to 10, so it is possible that for any given c value that the number of results might not be the same as for previous rows, so the assignment to the row could fail. Whether this happens or not could depend on the exact values used by the assignment to C such as by linspace or colon operator.

Also you can increase precision by adding 'maxdegree', 3 to the solve() call