Lesson 6-6 Warm-Up

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Lesson 6-6 Warm-Up
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Systems of Linear Inequalities (6-6)

• What is a system of linear inequalities?
• What is a solution of system of linear
  inequalities?

• system of linear inequalities two or more
  linear inequalities on a graph
• Solution of a System of Linear Inequalities a
  solution that makes all of the inequalities in a
  system true
• In the graph below, the lavendar-shaded area
  include all of the solutions of the system
  represented by x 3 and y ? -2 (in other words,
  it include all of the solutions that make both
  inequalities true).

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Systems of Linear Inequalities (6-6)

• What is a solution set?

• Solution Set the graph that shows the set of
  all solutions to the system
• Example What is the solution set of y ? 2x 5
  and 3x 4y ? 12 .
• The points where the two inequalities overlap
  shaded in lavender is the solution set to the
  system.

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Systems of Linear Inequalities (6-6)

• How can you describe the four quadrants of a
  coordinate grid with systems of linear
  inequalities?

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Systems of Linear Inequalities
LESSON 6-6
Additional Examples
Solve by graphing. y lt x 3 2x 4y
0
2x 4y 0
2x 2x
1
4y 2x
__ __
4 4
2
1 2
1y x 0
Check The point (1, 1) is in the region graphed
by both inequalities. See if (1, 1) satisfies
both inequalities.
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Systems of Linear Inequalities
LESSON 6-6
Additional Examples
(continued)
The coordinates of the points in the light blue
region where the graphs of the two inequalities
overlap are solutions of the system.
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Systems of Linear Inequalities
LESSON 6-6
Additional Examples
Write a system of inequalities for each shaded
region below.
blue region
Boundary lines y 4 and y x 2
1 2
The region lies below the boundary line, so the
inequality is y ? x 2 and y lt 4.
1 2
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Systems of Linear Inequalities
LESSON 6-6
Additional Examples
You need to make a fence for a dog run. The
length of the run can be no more than 60 ft, and
you have 136 feet of fencing that you can use.
What are the possible dimensions of the dog run?
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Systems of Linear Inequalities
LESSON 6-6
Additional Examples
(continued)
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Systems of Linear Inequalities
LESSON 6-6
Additional Examples
Suppose you have two jobs, babysitting, which
pays 5 per hour and sacking groceries, which
pays 6 per hour. You can work no more than 20
hours each week, but you need to earn at least
90 per week. How many hours can you work at each
job?
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Systems of Linear Inequalities
LESSON 6-6
Additional Examples
(continued)
The solutions are all the coordinates of the
points that are nonnegative integers that lie in
the region shaded light-blue and on the lines b
s 20 and 5b 6s 90.
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Systems of Linear Inequalities
LESSON 6-6
Lesson Quiz
Solve each system by graphing. 1. x 0 2.
2x 3y gt 12 3. y x 3 y
lt 3 2x 2y lt 12 2x 3y
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2 3
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Systems of Linear Inequalities
LESSON 6-6
Lesson Quiz
4. Write a system of inequalities for the
following graph.