It is possible that the regions do not intersect. When this occurs, there is no solution of
the system or the solution set is the empty set.
Empty Set The emPtY
set is also called the
null
set.
lt can be
represented by @ or {}.
Regions
@separate
the system of inequalities by graphing.
Solve
y>x*5
y<x-4
y- x+5
Graph both inequalities.
Since the graphs of the inequalities
do not overlap, there are no Points
in common and there is no solution
to the system.
The solution set is the emPtY set.
;flJ'Crid"a' Practice
28. y > lxl
" z1*
y\-^
2A.y. -4x+8
y<-4x+4
24
)-
Personal Tutor glencoe.com
Write and Use a System of lnequalities
$-Rml-wuH;rinft
Typical incoming freshmen
will spend more than
3 times as many hours
studying in college as
TIME MANAGEfiflENT Chelsea has final exams in calculus, physics, and history. She
has up to 25 hours to study for the exams. She plans to study history for 2 hours'
She needs to spend at least 7 hours studying for calculus, but over 14 is too much.
She hopes to spend between 8 and 12 hours on physics. Write and graph a system
of inequalities to represent the situation.
Calculus: at least 7 hours, but no more than 14
7<c<74
ct,
6
rn
c
16
in high school.
$owce: National Survey of
Student Engagement
Physics: at least 8 hours, but no more than
12
8<P<72
Chelsea has 25 hours available, and 2 of those
will be spent on history. She has up to 23 hours
left for calculus and physics.
c+P<23
o
-12
{,
r
o
-4
4
Graph all of the inequalities. Any ordered pair
in the intersection is a solution of the system.
One solution is 10 hours on physics and
12 hours on calculus.
#'Guided
3;
t2 16
2op
Hours Spent on Physics
Practice
Mr. and Mrs. Rodriguez are driving across the country with their
two children. They plan on driving a maximum of 10 hours each day.
Mr. Rodrigu", *ur-ris to drive at least 4 hours a day but no more than 8 hours
a day. Mrs-. Rodriguez can drive in between 2 and 5 hours per day. write
and graph a system of inequalities that represents this information.
TRAVEL
)
152
8
Chapter 3 Systems of Equations and lnequalities
Rersonal Tutor glenlgeJom