This is not necessarily intended to always be an easier method of solving systems and, in fact, it sometimes complicates the problems. The iterative process does involve some very beautiful mathematics and it occasionally offers a method of solution to systems that are otherwise analytically impossible to solve. The first activity presents the algorithm for the solution of any system of two linear equations and is suitable for Algebra I or Algebra II students. The second activity generalizes the algorithm to systems of equations in which one of the equations is linear and the other is any continuous and invertible function. The second part requires that students be familiar with inverses of various standard functions and is probably most appropriate for Algebra II or Trigonometry.
Transformational geometry is used to justify the algorithms.
The reason for this requirement stems from the process involved in iteration. Allow students to pick any initial value of x that they want to try. This value of x is called a seed and is denoted by . We now iterate our function using the non-identity equation in our system. An easy way to achieve this sequence of numbers using a TI calculator would be to first type the seed into your calculator and then press the key.