system of inequalities


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 2x - 6y < 12,="">x + 4y < 12,="" and="">x + 2y ≥ 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 of x + 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 of y ≥ - 3  is the half-plane on and above the solid line y = - 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