Learning Objectives:

__Math Tutoring on Solving Systems of Linear Inequalities__

A **system of inequalities **is a set of **inequalities** which includes multiple variables and solved with an exact specification of the values of all variables that satisfies all of the **inequalities** simultaneously. A system of **inequalities** can be solved either graphically or non-graphically.

The solution to a system of **linear inequalities **consists of the region for which any point** x, **satisfy the **linear equalities **of the system at the same time. So the steps to graphing the solution to a **system of linear inequalities **are as follows.

__Step one__**: Graph** and **shade** the solution to the first **linear inequalities.**

__Step two__**: Graph** and **shade** the solution to the second **linear equality **on the same coordinate plane. And the region that is double shaded is the solution to the system. It should be mentioned, if the number of inequalities, **n,** in the system is more than **2, **then we will look for the region shaded **n** times. So if it has three **inequalities**, you are looking for the region shaded three times and so on. And also, some systems may not have a solution.

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**Hook Questions:**

*1. **What is the difference between the system of equalities and system of inequalities?*

*2. **Define the system of linear inequalities.*

*3. **What are the methods to solve the system of linear inequalities?*

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