Systems of nonlinear equations

The  exercise appears under the Algebra II Math Mission. This exercise extends the concept of systems to equations that are not linear.

Types of Problems
There are two types of problems in this exercise:


 * 1) Determine the system from the possible graphs: This problem has a system of equations and four possible graphs. The student is asked to determine which of the four graphs models the system.Sone1.png
 * 2) Find the solution(s) to the system: This problem provides a system of equations of which at least one is not linear. The student is expected to find all solutions to the system of equations and select the correct answer from a multiple choice list.Sone2.png

Strategies
Knowledge of the various methods for solving systems of equations are encouraged to ensure success on this exercise.
 * 1) Although not necessary, substitution tends to be more intuitive than elimination on these systems.
 * 2) Matrices cannot be used, since the equations involved are non-linear.
 * 3) To improve efficiency, the solutions can be found by plugging in the possible answer choices (or points to graph).

Real-life Applications

 * 1) Most functions are not linear, so techniques for dealing with these types of functions becomes more important the further one advances in mathematics.