import numpy as np


def system_equations(variables):
    x, y = variables
    equation1 = np.sin(y) + 2 * x - 2
    equation2 = np.cos(x - 1) + y - 0.7
    return np.array([equation1, equation2])


def jacobian_matrix(variables):
    x, y = variables
    jacobian = np.array([[2, np.cos(y)], [-np.sin(x - 1), 1]])
    return jacobian


def newton_method(initial_guess, tolerance=1e-3, max_iterations=100):
    variables = initial_guess
    for iteration in range(max_iterations):
        equations = system_equations(variables)
        jacobian = jacobian_matrix(variables)

        delta = np.linalg.solve(jacobian, -equations)
        variables += delta
        if np.max(np.abs(delta)) < tolerance:
            return variables
    raise ValueError("The method did not converge")


def main():
    initial_guess = np.array([0, 0], dtype=float)
    solution = newton_method(initial_guess)
    print(f"Solution: x = {solution[0]}, y = {solution[1]}")


if __name__ == '__main__':
    main()