How can I solve two non linear equation with Newton_Raphson method?

Hello,

I am very new user of Matlab. I am facing problem to solve the following equation.

F(x,y) = x^2+2y^2-4=0 G(x,y) = xy-1=0

the code I have written,

%% Input initial value

x=2;

y=0;

Tolerance = 0.00001;

Error_max = 100 ;

%% Iteration

count = 0; while Error_max > Tolerance count = count + 1;

f1=x^2+2*y^2-4; f2=x*y-1; % Jacobian matrix J(1,1)= 2*x; J(2,1)= y ; J(1,2)= 4*y; J(2,2)= x;

f(x,y)=[x^2+2*y^2-4;x*y-1]; %% format long %

xnyn = [x;y]- J(x,y)\f(x,y) ;

xn=xnyn(1); yn=xnyn(2);

 Error = abs((xnyn -[x;y])/[x;y] ) ;
        Error_max= Error;

Result(count,1)=x; Result(count,2)=y; x=xnyn(1); y=xnyn(2);

    Result(count,4)=Jd;
    Result(count,5)=xn;
    Result(count,6)=yn;

end

 %%Print Results

 xn=num2str(xn);
 yn=num2str(yn);

 disp (count)
 disp (xn)
 disp (yn)

--------------------------------------------------------------------------------------- when I run the code, it gives me this message : >> newton_raphson_2eq Subscript indices must either be real positive integers or logicals.

Error in newton_raphson_2eq (line 30) f(x,y)=[x^2+2*y^2-4;x*y-1];

Can anyone please help me to solve this problem?

Thanks in advance.

Tanjina