1. Linear Inequalities in Two Variables
Chapter 4 Section 4
Linear Inequalities in Two Variables

2. Linear Inequality in Two Variables
Ax + By = C
Straight lines when graphed.
Replace the = symbol with an inequality
Linear Inequality in Two Variables

3. Examples
x + y > 2
5y ≤ 15
2x – y > 4

4. Solution of an inequality
Two variables
Ordered pair of real number that satisfy the inequality
Graph
Region, half plane
Solid line: line is part of the graph
Dashed line: not part of the graph

5. Solve Replace the inequality symbol with = Graph the line
Choose a test point.
True statement, shade that part of the half plane that contains the test point.

6. Practice
Solve and graph the solution set
2x – 3y < 6

7. Graph the solution set
2x + y > 6
x ≤ - 4

8. System of Linear Inequalities
Two or more linear inequalities
Solution
Ordered pair that satisfies each inequality in the system

9. Graph the solution Solution Replace the inequality with =
Graph each line
Lines intersect, so pick a test point in each region.

10. One more
Graph the solution set

11. Graph the Solution set
c) d)