Example 3
Graphing a System of Linear Inequalities
Graph the system of inequalities.
y > –x – 3
Inequality 1
y ≤ 2x + 1
Inequality 2
SOLUTION
STEP 1 Graph the first inequality in the system. Use
red for y > –x – 3.
Example 3
Graphing a System of Linear Inequalities
STEP 2 Graph the second inequality in the system.
Use blue for y ≤ 2x + 1.
The graph of the system is the intersection of the red and blue
regions, which is the purple region.
STEP 3 Identify the region that is common to both
graphs. All ordered pairs in this region are
solutions of the system of inequalities.
Guided Practice
for Example 3
Graph the system of inequalities.
5. y < x + 2
y ≥ –2x – 1
ANSWER
Guided Practice
for Example 3
Graph the system of inequalities.
6. x + y > 5
y ≤ 3x + 4
ANSWER
Guided Practice
for Example 3
Graph the system of inequalities.
7. y ≤ 4x – 2
5x + y < 1
ANSWER
Guided Practice
for Example 3
8. REASONING
Graph the system of inequalities consisting of
y > x + 3 and x – y > 2. What does the graph tell
you about the system’s solutions? Explain.
Guided Practice
for Example 3
ANSWER
there are none; the inequalities have no common
solutions.