Algebra 1 Common Core Student Edition, Grade 8-9

@ Common Core Stale Standards

Q cl_ ry_c _£ A -R E I.D .1 2 G r a p h ... the solution set to a system o f

OVbienib Ul linear in equalities in tw o variables as the intersection

I • • ° ^ e corresponding half-planes.

L i n e a r I n e q u a 1 111 e s mpi.mp 2 .mpb, mp \ m r

Object ives To solve systems of linear inequalities by graphing

To model real-world situations using systems of linear inequalities

Se e how many

combinat ions

you can find

that satisfy this

si t u at i o n.

Get t i n g Read y!

Yo u w an t t o b u y a t l e a st 6 n ew r i n g

tones from a Web site, but you cannot

sp en d m o r e t h an $ 1 5. How m any

premium ring tones and how many t o p - 10

ring t ones can you b uy? Explain how you

found your answer.

RI N G TON ES

Pr em i u m $ i .5 0 BUY N O W

TOP 1 0 $ 3 .0 0 BUY N O W

PR A C T I C ES ^ system °f linear inequalities is made up of two or more linear inequalities. A

Lesso n

Vocabulary

syst em o f l i n ear

inequalities

so lu t i o n o f a

syst em o f l i n ear

inequalities

so l u t i o n o f a syst em o f l i n ear i n eq u al i t i es is an ordered pair that makes all the

inequalities in the system true. The graph of a system of linear inequalities is the set of

points that represent all of the solutions of the system.

Esse n t i a l U n d e r st a n d i n g You can graph the solutions of a system of linear

inequalities in the coordinate plane. The graph of the system is the region where the

graphs of the individual inequalities overlap.

Have you seen a

problem like this

before?

Ye s. Th e so l u t i o n o f a

system of equations is

sho wn by t he i nt er sect i on

of two lines. The

solutions of a system of

inequalities are shown by

the intersection of two

shad ed ar eas.

Gr ap h i n g a Syst em of In eq u alit ies

What is the graph of the system? y < 2x - 3

2x + y > 2

Graph y < 2x - 3 and 2x + y > 2.

\ 1

Th e b lu e reg io n

represents solutions of

2x + y > 2.

Th e yel l o w reg io n

represents solutions of

y < 2x - 3.

Th e g r een reg i o n

represents solutions of

both inequalities.

The system’s solutions lie in the green region where the graphs overlap.

400 Chapter 6 Sy st e m s o f Eq u a t i o n s a n d I n e q u a l i t i e s