#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Sat Sep 27 15:31:11 2025

@author: christian
"""

u = lambda x, y: x**2 + x*y - 10
v = lambda x, y: y + 3*x*y**2 - 57

# Initial guesses
x_0 = 1.5
y_0 = 3.5

# Evaluate partial derivatives at initial guesses
dudx = 2*x_0+y_0
dudy = x_0

dvdx = 3*y_0**2
dvdy = 1 + 6*x_0*y_0

# Find determinant of the Jacobian
det = dudx * dvdy - dudy * dvdx

# Values of functions valuated at initial guess
u_0 = u(x_0,y_0)
v_0 = v(x_0,y_0)

# Substitute into newton-raphson equation
x_1 = x_0 - (u_0*dvdy-v_0*dudy) / det
y_1 = y_0 - (v_0*dudx-u_0*dvdx) / det

print(x_1)
print(y_1)