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?'
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)
Below is the graph of the following system of inequalities:
y > – x
y > x + 1
From the picture can you determine which area is the solution of this system?