**Definition of System of Inequalities**

- A system of inequalities is a set of two or more inequalities with the same variables, graphed in the same coordinate plane.

**Examples of System of Inequalities**

- The figure below shows the graph of the system of inequalities 2
*x*- 6*y*< 12,="">*x*+ 4*y*< 12,="" and="">*x*+ 2*y*≥ 8.

**Solved Example on System of Inequalities**

Which of the graphs defines the system of inequalities,

x+y< 3,="" -="">x+ 2y≤ 10,y≥ - 3?

Choices:

A. Graph-1

B. Graph-2

C. Graph-3

D. Graph-4

Correct Answer: A

Solution:

Step 1:Graph all the three inequalities in the same coordinate plane.

Step 2:The graph ofx+y< 3 is="" the="" half-plane="" below="" the="" dashed="" line="">x+y= 3.

Step 3:The graph of - 5x+ 2y≤ 10 is the half-plane on and below the solid line - 5x+ 2y= 10.

Step 4:The graph ofy≥ - 3 is the half-plane on and above the solid liney= - 3.

Step 5:The graph of the system is the intersection of the three half planes as shown in the graph.

Step 6:Graph-1 is the correct answer.

**Related Terms for System of Inequalities **

- Inequalities
- Variables
- Coordinate Plane