Cambridge International Mathematics

Linear inequalitiesdefine regions of the Cartesian plane.

Example 3 Self Tutor

Write inequalities to represent the following unshaded regions:

abc

de f

abc

de f

B LINEAR INEQUALITY REGIONS [7.7]

O

y

x

x¡=¡3

R

O

y

x

x¡=¡2

R

y¡=¡4

O

y

x

R

O

y

x

R

2

O

y

x

R

-3

O

y

4 x

R

O

y

x

3

-2

R

O

y

x

R

2

3

x=3. This region is specified by the linear inequalityx> 3 ,

than 3.

To illustrate this region we shade out allunwantedpoints. This

We consider the boundary separately.

We use a solid boundary line to indicate that points on the

boundary are wanted.

If the boundary is unwanted, we use a dashed boundary line.

For example, to illustrate the region specified by x> 2 and

y> 4 , we shade the region on and to the left of the linex=2,

and the region on and below the line y=4. The regionR

left completely unshaded is the region specified by x> 2 and

y> 4. The lines x=2and y=4are dashed, which

indicates the boundaries are not included in the region.

inequalities define a region, asRis the region left unshaded.

makes it easier to identify the required regionRwhen several

since all points withinRhavex-coordinates which are more

Consider the regionRwhich is on or to the right of the line

x 60 and y 60 y> 2 x>¡ 3

06 x 64 ¡ 2 <y< 306 x 63 and 06 y 62

Inequalities (Chapter 32) 641

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Y:\HAESE\IGCSE01\IG01_32\641IGCSE01_32.CDR Friday, 31 October 2008 9:23:08 AM PETER