Using Newton's Method to solve system of equations

Question

I am getting an error that just gets stuck formatting notepad, i don't think there's anything in my code that is wrong, but I'm never sure.

f[x_, y_] = xy^2 + x^3 y;
fx[x_, y_] = 2 xy^2 + y^3;
fy[x_, y_] = 2 x^2 y + 3 xy^2;

g[x_, y_] = x^2 y - xy^4;
gx[x_, y_] = 2 xy - y^4;
gy[x_, y_] = x^2 - 4 xy^3;

u = 1.6;
v = 0.7;
For[i = 0, i < 7, i++,
  d = fx[u, v] gy[u, v] - fy[u, v] gx[u, v];
  h = (g[u, v] fy[u, v] gy[u, v])/d;
  k = (f[u, v] gx[u, v] - g[u, v] fx[u, v])/d;
  u = u + h;
  v = v + k;
  Print[u, " ", v, " ", f[u, v], " ", g[u, v]]];

Answer 1

The following errors:

Wrong: f[x_, y_] = xy^2 + x^3 y; Correctly: f[x_, y_] := x*y^2 + (x^3)*y;

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Working code:

 Clear[f, fx, fy, g, gx, gy,d,h,k,u,v];
f[x_, y_] := x*y^2 + (x^3) y;

fx[x_, y_] := 2 x*y^2 + y^3;
fy[x_, y_] := 2 (x^2) y + 3 x*y^2;

g[x_, y_] := (x^2) y - x*y^4;
gx[x_, y_] := 2 x*y - y^4;
gy[x_, y_] := x^2 - 4 x*y^3;

u = 1.6;
v = 0.7;

For[i = 0, i < 7, i++,
  d = fx[u, v] gy[u, v] - fy[u, v] gx[u, v];
  h = (g[u, v] fy[u, v] gy[u, v])/d;
  k = (f[u, v] gx[u, v] - g[u, v] fx[u, v])/d;
  u = u + h;
  v = v + k;
  Print[u, " ", v, " ", f[u, v], " ", g[u, v]]
  ];