Solving and Plotting Arrays

I am trying to find and plot the values of xSol and ySol by using x and y arrays as follow:

clc
clear all

% DME COORDINATES
x1= 2;  y1= 10; % DME 1
x2= 15; y2= 30; % DME 2
x3= 20; y3= 3;  % DME 3

% ASSUMED POSITION OF OBJECT
x = [10,25,31,35,40];
y = [20,30,41,49,56];

% DISTANCE OF OBJECT TO DMEs
r1 = sqrt((x-x1).^2+(y-y1).^2);
r2 = sqrt((x-x2).^2+(y-y2).^2);
r3 = sqrt((x-x3).^2+(y-y3).^2);

% EQUATIONS
syms x y
eqn1 = 2*x*(x2-x1)+2*y*(y2-y1) == (r1.^2) - (r2.^2) + (x2.^2) - (x1.^2) + (y2.^2) - (y1.^2);
eqn2 = 2*x*(x3-x1)+2*y*(y3-y1) == (r1.^2) - (r3.^2) + (x3.^2) - (x1.^2) + (y3.^2) - (y1.^2);

sol = solve([eqn1, eqn2], [x, y]);
i=length(x);
j=length(y);
for k=1:i
    
    xSol = sol.x(k);
end

Index exceeds the number of array elements. Index must not exceed 0.

Error in indexing (line 1075)
R_tilde = builtin('subsref',L_tilde,Idx);

for m=1:j
    ySol = sol.y(m);
end

plot(xSol,ySol,'LineWidth',4)

But it gives me error saying index exceeds. Kindly help!

[Jeffrey Clark]

I don't have the Symbolic Math Toolbox, but the documentation indictates If solve returns an empty object, then no solutions exist. So the sol.x and sol.y would be empty. You should use the length of sol.x and sol.y for i and j, not the length of x and y.

[Star Strider]

There is no solution —

% DME COORDINATES
x1= 2;  y1= 10; % DME 1
x2= 15; y2= 30; % DME 2
x3= 20; y3= 3;  % DME 3

% ASSUMED POSITION OF OBJECT
x = [10,25,31,35,40];
y = [20,30,41,49,56];

% DISTANCE OF OBJECT TO DMEs
r1 = sqrt((x-x1).^2+(y-y1).^2);
r2 = sqrt((x-x2).^2+(y-y2).^2);
r3 = sqrt((x-x3).^2+(y-y3).^2);

% EQUATIONS
syms x y
eqn1 = 2*x*(x2-x1)+2*y*(y2-y1) == (r1.^2) - (r2.^2) + (x2.^2) - (x1.^2) + (y2.^2) - (y1.^2)

eqn1 = 

eqn2 = 2*x*(x3-x1)+2*y*(y3-y1) == (r1.^2) - (r3.^2) + (x3.^2) - (x1.^2) + (y3.^2) - (y1.^2)

eqn2 = 

[A1,b1] = equationsToMatrix(eqn1)

A1 = 

b1 = 

[A2,b2] = equationsToMatrix(eqn2)

A2 = 

b2 = 

A = [A1;A2]

A = 

b = [b1;b2]

b = 

[x,RankA] = linsolve(A,b)

Warning: Solution does not exist because the system is inconsistent.

x = 

RankA = 

2

.

[Curious]

Well, great.. Thanks alot Star Strider

[Star Strider]

My pleasure!

I just wish I could have found a solution for you!

[Curious]

I don't need a solution, having no solution is just a case. I am making a program that can solve this system of equations on different positions of x,y and plot those points. Well, at some points the systems may say it has no solution;)