Learning Objectives:

__Math Tutoring on Solving Systems of Nonlinear Equations__

In this section, we are going to be looking at **nonlinear systems of equations. **A **nonlinear system of equations** is a system in which at least one of the variables has an exponent other than **1 and /or** there is a product of variables in one of the equations or in other words a **nonlinear system** is a collection of equations that may contain some equations of line, but not all of them. To solve these systems we will use either the **substitution method **or** elimination method** that we first looked at when we solved **systems of linear equations. **The main difference is that we may end up getting **complex solutions** in addition to **real solutions**. Just as we saw in solving systems of two equations the real solutions will represent the coordinates of the points where the graphs of the two functions intersect. Since **nonlinear equations** are difficult to solve, so nonlinear systems are commonly **approximated **by** linear equations** and the method is known as **linearization.**

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**Hook Questions:**

*1. **What is a nonlinear system?*

*2. **What is a nonlinear equation?*

*3. **What is an example of a nonlinear equation?*

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