Chapter 6, Problem 22P

Determine the roots of the following simultaneous nonlinear equations using (a) fixed-point iteration and (b) the Newton-Raphson method:

$\begin{array}{l}y=-x^2+x+0.75\\ y+5xy=x^2\end{array}$

Employ initial guesses of $x=y=1.2$ and discuss the results.