Using Fsolve to find value of 2 variables with different functions

I am trying to solve a system of equations with variables xp and xq. Each is defined by a different function and has a different value at 4 stages: xp(1), xp(2), xp(3), xp(4) ect.

I tried to find a solution by writing out all the equations and using vpasolve but there were 16 equations and no solution was found after 20 minutes. I have found similar examples using fsolve but I don't know how to adapt this code to solve for two variables (xp and xq). Any help or suggestions of an alternative approach would be appreciated.

function x =LLESolver(xp,xq)
N=4
x0=ones(N*2,1);
[x,fval]=fsolve(@LLE,x0,xp,xq)


function P=LLE(xp,xq)
xpa = 1.2; % kg/m3, conc. of solute in entering aqueous stream 
ypb = 0.0; 
L = 2.0; % m3/s
V = 1.0; % m3/s
N = 4;
xqa = 1.6; % kg/m3, conc. of solute in entering aqueous stream 
yqb = 0.0;% kg/m3, conc. of solute in entering organic stream 
for i=1:4
    if i==1
        P(i)=L*(xpa-x(i))-V*(EquRel_P(i)-EquRel_P(i+1))
    elseif i==N
            P(i)=L*(xp(i-1)-x(i))-V*(EquRel_P(i)-ypb)
    else  
                P(i)=L*(xp(i-1)-x(i))-V*(EquRel_P(i)-EquRel_P(i+1))
    end
end
for i=5:8
    if i==5
        P(i)=L(xqa-x(i))-V*(EquRel_Q(i)-EquRel_Q(i+1))
    elseif i==8
            P(i)=L*(x(i-1)-x(i))-V*(EquRel_Q(i)-yqb )
    else  
                P(i)=L(xqa-x(i))-V*(EquRel_Q(i)-EquRel_Q(i+1))
    end
end

[madhan ravi]

Ruth that’s ruthless!

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Walter Roberson]

function x =LLESolver(xp,xq)
N = 4;
x0 = ones(N*2,1);
[x,fval]=fsolve(@(x) LLE(x, xp, xq), x0)

function P = LLE(x, xp, xq)

[Ruth]

Thanks Walter, I have implemented this. There was a mistake in the LLE part, x(i) was meant ot be xp(i). So now there are no x s in the function should it read as this?

function x =LLESolver(xp,xq)

N = 4;

x0 = ones(N*2,1);

[x,fval]=fsolve(@(x) LLE(xp, xq), x0)

function P = LLE(xp, xq)

Either way I'm getting:

Not enough input arguments.

Error in LLESolver (line 26)

[x,fval]=fsolve(@(x) LLE(x,xp,xq),x0)

Do you know where the problem may be? Could it be the functions EquRel_P and EquRel_Q?

Thanks for your help

[Walter Roberson]

[x,fval]=fsolve(@(xp) LLE(xp, xq), x0)

with

function P = LLE(xp, xq)

However, what do you want to do with the xp that was passed into LLESolver ?

[Ruth]

I want to solve the simultaneous equations for both xp and xq. Can fsolve do that?