Show how the secant method can be used to solve systems of equations such as those in Co...

Show how the secant method can be used to solve systems of equations such as those in Computer Exercises 3.2.21– 3.2.23.

Computer Exercises 3.2.21

Consider the nonlinear system

Using a software package that has 2D plotting capabilities, illustrate what is going on in solving such a system by plotting f (x, y), g(x, y), and show their intersection with the (x, y)-plane. Determine approximate roots of these equations from the graphical results.

Computer Exercises 3.2.22

Solve this pair of simultaneous nonlinear equations by first eliminating y and then solving the resulting equation in x by Newton’s method. Start with the initial value x₀ = 1.0.

Computer Exercises 3.2.23

Using Equations (6) and (7), code Newton’s methods for nonlinear systems. Test your program by solving one or more of the following systems: