Mastering Linear Inequalities in 2 Variables

1. Linear Inequalities in 2 Variables 3.3

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: -2x – 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