1. Linear Inequalities in 2 Variables
3.3
Linear Inequalities in 2 Variables

2. OBJECTIVES: Solve and Graph a linear inequality in 2 variables.
Use a linear inequality in 2 variables to solve real-world problems.

3. Definition: Linear Inequality in 2 Variables
Using variables x & y, it is any inequality that can be written in one of the forms below, where A ≠ 0 and B ≠ 0.
Ax + By ≥ C
Ax + By > C
Ax + By ≤ C
Ax + By < C

4. SOLUTION… Ordered Pair  (x, y)
A region of the coordinate plane & is called a half-plane bounded by a boundary line.

5. Graph: y < x + 2 Graph the line.
Use a dashed line because the values on this line are not included in the solution
Choose a point such as (0, 0) to test.
Since (0, 0) satisfies the inequality, shade the region that contains the point

6. Graph: y ≥ -2x + 3 Graph the boundary line.
Use a solid line because the values on this line are included in the solution
Choose a point like (0, 0) to test
Since (0, 0) does not satisfy the inequality, shade the region that does not contain this point.

7. Extra Examples, If Needed…
y > -2x – 2
y ≤ 2x + 5

8. GRAPH: x – 3y ≤ 3
Sometimes, you may need to solve for for y before graphing.

9. Graph: 3x – 4y ≥ 4

10. SOLUTION to 1 variable equations
A half-plane
Graph: x > -2

11. Example
Graph: y ≤ -1

12. ACTIVITY
PG. 175