Graphing systems of inequalities is like graphing systems of equations. The main difference being that the intersection of the different graphs can be very large as opposed to a single point in equations. In other words, the solution to a system of inequalities is an area of the graph that satisfies all the conditions of the system.

 

Example

Graph the system

y > x² + 2

y > 2 x + 4

 

Graph the first inequality.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

On the same graph, graph the next inequality, y ≤ 2 x + 4.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The area that is shaded in twice is the area that meets both conditions.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer!

 

 

 

 

 

 

Example

Graph the following system

 

y –x ≥ 2

x ≥ -3

x ≤ 2

y ≤ 5

 

Graph all of the inequalities on the same graph. The area that matches all of these inequalities is the solution.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer!

Note- All the points that are shaded in the graph are solutions. The points ( -2, 3), ( -1, 2), and (3, 4) are all in the shaded area and therefore are possible solutions to the system.