A System of linear inequalities is simply two or more linear inequalities on the same plane. In other words, a system of linear inequalities is just two or more inequalities together.

The easiest way to remember what 'system' means in this context is by answering the following question: 'Does the word *system* ever refer to just one thing or does *system* always refer to more than one thing?

The answer is 'more than one thing' Likewise a 'system of linear inequalities' is 'more than one linear inequality'

**Interactive** System

of Linear Inequalities

Click and drag on the points below and the system of linear inequalities will adjust accordingly.

(Full sized interactive system of linear inequalities)

Below are the graphs of the linear inequalities: y < x + 1 and y> x

Pictured above is the system of inequalities made up the same two linear inequalities:

y < x + 1

y > x

When we take both of the linear inequalities pictured above and graph them on same Cartesian plane,
we get a system of linear inequalities. The **solution** of this system is the yellow region
which is the area of overlap. In other words, the solution of the system is the region where both
inequalities are true. The **y coordinates** of all points in the yellow region are **both** greater than x+1 as well as less than x.

**Example**

of a system of Linear Inequalities

The picture below shows a system of linear inequalities.

On the left is the graph of two linear inequalities. What is the solution to this system of linear inequalities?

(Reminder: the solution is the region that **both** inequalities cover)