A AT ( H )

9.5 SYSTEMS OF INEQUALITIES

EX 1) GRAPH THE INEQUALITY

Remember!

• use a dashed line for < or > and a solid line for ≤ or ≥

• Test one point in each region to see where to shade

• A solution is a region (solution set) – not the intersection point like in a system of equations.

Dashed Line

A solution is (0,2) so shade above the line

2 1y x

EX 2) GRAPH THE INEQUALITY

Solid Line

A solution is (-2,-2) so shade below the line

2 3y x

EX 3) GRAPH THE SYSTEM OF INEQUALITIES

Graphing a System• Sketch the graph of

each individual inequality.

• Find the region that is common to every graph in the system. This will be the solution set.

First inequality: solid lineSecond inequality: dashed line

A solution to BOTH inequalities is (-1, 0)

2 32

y xy x

EX 4) GRAPH THE SYSTEM OF INEQUALITIES

11

22 4

y x

y x

No Solution!

There is no solution set that satisfies BOTH inequalities

EX 5) GRAPH THE SYSTEM OF INEQUALITIES AND FIND THE VERTICES OF THE TRIANGLE.

16

12 32

x yx yy x

Test solution points.

(0, 0) is a solution set, so inside the triangle is shaded.

To find the vertices, find the intersections of all 3 lines using your calculator, or solving each system of 2 equations (there will be 3 systems total).

Vertices: (-4, 3) (8, 2) and ( , - )

EX 6) GRAPH THE SYSTEM OF INEQUALITIES AND FIND THE VERTICES OF THE TRIANGLE.

3 2 6

4 2

2 3

x y

x y

x y

(0, 1) is a solution set, so inside the triangle is shaded.

Vertices: (0, 3) (-2, 0) and ( , ) or )

EX 7) GRAPH THE SYSTEM OF INEQUALITIES

1

1 3

x y

x

A solution point is (0, 0)

EX 8) GRAPH THE SYSTEM OF INEQUALITIES

1

2 1 3

x y

y x

EX 9) GRAPH THE SYSTEM OF INEQUALITIES

2 2 16x yy x

EX 10) GRAPH THE SYSTEM OF INEQUALITIES

2 11

x yx y

PRACTICE

• pg. 27 – 31, 35, 37, 49