format long e
p=[-2 3]';
n0=100;
tol=10^(-10);

f1=@(x) x(1)+2*x(2)+0.03*sin(x(1)+x(2))-4;
f2=@(x) 5*x(1)+6*x(2)+0.07*cos(x(1)-x(2))-8;
df1dx1=@(x) 1+0.03*cos(x(1)+x(2));
df1dx2=@(x) 2+0.03*cos(x(1)+x(2));
df2dx1=@(x) 5-0.07*sin(x(1)-x(2));
df2dx2=@(x) 6+0.07*sin(x(1)-x(2));

while i<=n0
  fp=[f1(p) f2(p)]';
  j=[df1dx1(p) df1dx2(p);df2dx1(p) df2dx2(p)];
  y=-inv(j)*fp;
  p=p+y;
  if norm(y,inf)<tol
    p(1)
    p(2)
    return
  end
  i=i+1;
end