This problem focuses on the system of simultaneous equations (): x^x + y^y = 1000, x^y + y^x = 100. see the two curves given by equations () in the text [1, ch. 14, problems plus, problem 6(b), p. 1026]. choose any initial point (x_0, y_0) anywhere near either solution (x_*, y_*) of the system of equations (). complete at least one iteration of newton's method to compute the next point, (x_1, y_1). if you compute by hand, then choose a computationally convenient initial point (x_0, y_0). if you use a computer, then supply a paper or electronic copy of your program, documenting the fact that it carries out newton's method. for this problem you need not achieve an accuracy of six significant digits. you need only complete at least one iteration, starting with numerical values for (x_0, y_0), terminating with numerical values for (x_1, y_1). newton's method with one variable is also in the calculus text.