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System
of Linear Inequalities
A
line divides a coordinate plane into three parts, two half planes
(Regions I and II) and the line itself. Sometime a half plane could
includes the line.
 
Two
steps to solve a system of linear inequalities with two variables:
1. Graph each inequality on the same set of coordinate-axes.
2. Find the intersection of the regions of solutions of each individual
inequality and this overlapped region is
the answer to the system..
Ex
1: Solve the system
of linear inequalities: 
Sol
: 1.
Graph each each boundary line on the same set of coordinate-axes.
2. Choose
0 (since 0 is not on both lines.) as the test value to determine
the solution set for each
inequality.
 
3.
Find the intersection of the solution set found in step 2.
4. The
answer to this example is the shaded region as shown in figure below.
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