Post on 10-Apr-2018
8/8/2019 Graphing Inequalities Day8
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Solving Systems of
Equations
Graphing Linear Inequalities
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Objectives How dowe graph an inequality
Define a boundary line
Graphing a boundary line
Define the solution for a system ofinequalities
Find the s
oluti
on
of a system
of inequalities
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What isthe solution of an
inequality
Solution of an inequality are all the
ordered pairs (points) that make theinequality true.
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Graphing InequalitiesConsider the inequality
y x
66
44
22
22
11 4433 6655
11
33
55
y = x Graph
Boundary line
REMEMBER: Solution are allthe ordered pairs (points) thatmake the inequality true.
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Graphing InequalitiesConsider the inequality
y x
66
44
22
22
11 4433 6655
11
33
55
1. Pick two points from eachside of the graph
(4,1)
(1,3)
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Graphing InequalitiesConsider the inequality
y x
66
44
22
22
11 4433 6655
11
33
55
(4,1)
(1,3)
2. Check points if they makeinequality true.
(1,3) y xsubstitute into
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Graphing InequalitiesConsider the inequality
y x
66
44
22
22
11 4433 6655
11
33
55
(4,1)
(1,3)
2. Check points if they makeinequality true.
(1,3) y xsubstitute into
3 1
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Graphing InequalitiesConsider the inequality
y x
66
44
22
22
11 4433 6655
11
33
55
(4,1)
(1,3)
2. Check points if they makeinequality true.
(1,3) y xsubstitute into
3 1
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Graphing InequalitiesConsider the inequality
y x
66
44
22
22
11 4433 6655
11
33
55
(4,1)
(1,3)
2. Check points if they makeinequality true.
(4,1) y xsubstitute into
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Graphing InequalitiesConsider the inequality
y x
66
44
22
22
11 4433 6655
11
33
55
(4,1)
(1,3)
2. Check points if they makeinequality true.
(4,1) y xsubstitute into
1 4
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Graphing InequalitiesConsider the inequality
y x
66
44
22
22
11 4433 6655
11
33
55
(4,1)
(1,3)
2. Check points if they makeinequality true.
(4,1) y xsubstitute into
1 4 X
X
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Graphing InequalitiesConsider the inequality
y x
66
44
22
22
11 4433 6655
11
33
55
(4,1)
(1,3)
3. Shade the side where the correctpoint lies.
X
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Graphing InequalitiesConsider the inequality
y x
66
44
22
22
11 4433 6655
11
33
55
(1,3)
3. Shade the side where the correctpoint lies.
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Graphing InequalitiesConsider the inequality
x - 2y 4
33
11
22--11 11 4433 6655
--22
22
x - 2y = 4 Graph
y = x - 212
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Graphing InequalitiesConsider the inequality
x - 2y 4
33
11
22--11 11 4433 6655
--22
22
x - 2y = 4 Graph
TEST POINTS !!
(0,1)
(6,0)
y = x - 212
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Graphing InequalitiesConsider the inequality
x - 2y 4
33
11
22--11 11 4433 6655
--22
22
(0,1)
(6,0)
(0,1)substitute into
x - 2y 4
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Graphing InequalitiesConsider the inequality
x - 2y 4
33
11
22--11 11 4433 6655
--22
22
(0,1)
(6,0)
(0,1)substitute into
x - 2y 4
0 - 2(1) 4
-2 4
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Graphing InequalitiesConsider the inequality
x - 2y 4
33
11
22--11 11 4433 6655
--22
22
(0,1)
(6,0)
(6,0)substitute into
x - 2y 4
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Graphing InequalitiesConsider the inequality
x - 2y 4
33
11
22--11 11 4433 6655
--22
22
(0,1)
(6,0)
(6,0)substitute into
x - 2y 4
6 - 2(0) 4
6 4 X
X
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Graphing InequalitiesConsider the inequality
x - 2y 4
33
11
22--11 11 4433 6655
--22
22
(0,1)
(6,0)
X
SHADE CORRECT REGION !!
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Examples
66
44
22
22
11 4433 6655
11
33
55
3y - 2x 91.
y = x + 32
3 GRAPH
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Examples
66
44
22
22
11 4433 6655
11
33
55
3y - 2x 91.
y = x + 32
3 GRAPH
TEST!!
(0,5)(0,5)
(3,0)
X
3(5) - 2(0) 9
15 - 0 9
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Examples2.
x - 3y > -3
y = x + 11
3
66
44
22
22
11 4433 6655
11
33
55
Graph
TEST!!
(0,5) (0,5)
0 - 3(5) > -3
0 - 15 > -3
X
X
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Solving a system of
Inequalities
Consider the system
x + y -1-2x + y < 2
33
11
22
--11
11 33
22
--22--33 --11
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Solving a system of
Inequalities
Consider the system
x + y -1-2x + y < 2
33
11
22
--11
11 33
22
--22--33 --11
TEST: (0,0)
Graph
0 + 0 -10 -1
(0,0)
y = - x - 1
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Solving a system of
Inequalities
Consider the system
x + y -1-2x + y < 2
33
11
22
--11
11 33
22
--22--33 --11
Graph
TEST: (0,0)-2(0) + 0 < 2
0 < 2
y = 2x + 2
(0,0)
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33
11
22
--11
11 33
22
--22--33 --11
33
11
22
--11
11 33
22
--22--33 --11
x + y -1 -2x + y < 2
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Solving a system of
Inequalities
Consider the system
x + y -1-2x + y < 2 33
11
22
--11
11 33
22
--22--33 --11
SOLUTION:
Lies where the two shadedregions intersect eachother.
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Solving a system of
Inequalities
Consider the system
-2x + 3y < -65x + 4y < 12
--11
33
11
22
--22
Graph
y = x - 223
3322 44--11--22 11TEST: (0,0)(0,0)
-2(0) + 3(0) < -6
0 < -6 X
X
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Solving a system of
Inequalities
Consider the system
-2x + 3y < -65x + 4y < 12
--11
33
11
22
--22
Graph
y = - x + 354
3322 44--11--22 11TEST: (0,0)5(0) + 4(0) < 12
0 < 12
(0,0)
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Solving a system of
Inequalities
Consider the system
-2x + 3y < -65x + 4y < 12
--11
33
11
22
--22
Graph
3322 44--11--22 11
(0,0) SOLUTION:
Lies where the two shadedregions intersect eachother.
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Solving a system of
Inequalities
Consider the system
-2x + 3y < -65x + 4y < 12
--11
33
11
22
--22
Graph
3322 44--11--22 11
(0,0) NOTE:
All order pairs in darkregion are true in bothinequalities.
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Solving a system of
Inequalities
Consider the system
x - 4y 124y + x 12
(0,0)
101088 1212664422
--22
66
22
44
--44
--66
TEST: (0,0)
(0) - 4(0) 120 - 0 12
0 12
Graph
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Solving a system of
Inequalities
Consider the system
x - 4y 124y + x 12
(0,0)
101088 1212664422
--22
66
22
44
--44
--66
TEST: (0,0)
4(0) + (0) 120 12
Graph
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HOMEWORK
Finish pg. 289 #8-16(solve the system ofinequalities by graphing)
#19 and 20.
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Problem ModelPatricios family, on average, drives their SUV more thantwice as many miles as they drive their car. His familys caremits 0.75 pounds ofCO2 per mile and the SUV emits 1.25
pounds ofCO2 per mile. Patricio is concern with theenvironment and convinces his family to limit the total CO2emissions to less than 600 pounds per month. How manymiles can they drive their car and SUV to meet this limit?
x
y
= SUV miles
= Car miles> 2yx
0.75y 1.25x 600
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Problem Model> 2yx
0.75y 1.25y 600
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Problem ModelThe science club can spend at most $400 on a field trip to adinosaur exhibit. It has enough chaperones to allow at most100 students to go on the trip. The exhibit costs $3.00 for
students 12 and under and $6.00 for students 12 and over.How many students 12 years and under can go if 20students over 12 go?
x
y
= Students 12 and under
= Students 12 and over4y3x 400+
yx 100+
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Problem Model
4y3x 400+
yx 100+
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Now you try
x
y
= front-page ads
= inside-page ads1y2x 30+
yx 20+
The Math Club want to advertise their fundraiser eachweek in the school paper. They know that a front-page ad
is more effective than an ad inside the paper. They havea total of $30 budget for advertising. It costs $2 for eachfront-page ad and $1 for each inside-page ad. If the clubwants to advertise at least 20 times, what are the differentpossibilities for the number of front-page and inside-page
ads.
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Now you try
1y2x 30+
yx 20+