systems of inequalities...graphing systems of inequalities 2 october 07, 2013 oct 6-9:38 pm graph...
TRANSCRIPT
Graphing Systems of Inequalities
1
October 07, 2013
Oct 7-7:38 AM
Warm-Up 10/7/13
1. The junior class sold 120 turkey dinner plates and 200 chicken dinner
plates for a total of $2,150. The senior class sold 100 turkey plates and 300
chicken plates, raising $2,625. What was the cost of each turkey dinner plate?
2. The drama club is selling $ckets to a play for $10 each. The cost to rent
the theater and costumes is $500. In addi$on the printers are charging $1
to print the $ckets. How many $ckets must the drama club sell to make a
profit?
Oct 6-8:57 PM
Graph the solution set for
Linear Inequalities in Two Variables
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
x
y
0
0
Oct 6-9:03 PM
PointAbove or Below
the Line?Inequality True or False?
(0,0) Above False
(5,0)
(0,3)
(4,2)
(6,1)
The solutions of lie on or
__________
Oct 6-9:11 PM
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
x
y
The shaded region and the boundary line make
up the graph
The solution area
is referred to as
a half-plane.
1. How would the graph of be like the
graph of ? How would it be different?
2. Would the points on the boundary line
be included in the graph of the inequality ?
Why or Why not?
Oct 6-9:24 PM
3. Error Analysis A student says that you
shade above the boundary line when the
inequality is or and you shade below it
when the inequality is or . Use the
example to explain why this is not always true.
Oct 6-9:26 PM
To graph a linear inequality in the
coordinate plane:
1. Graph the boundary line.
2. Choose a test point (x,y) that is not on the line.
Determine if the statement is true or false.
3. If the inequality is true for the test point,
shade the half plane that is on the side of
the boundary line with the test point. If not,
shade on the opposite side of the line.
Graphing Systems of Inequalities
2
October 07, 2013
Oct 6-9:38 PM
Graph the inequality
-10 -8 -6 -4 -2 0 2 4 6 8 10
-10
-8
-6
-4
-2
2
4
6
8
10
x
yEquation for the
boundary line:
_____________
Test a point (0,0)
7( )- <13
Oct 6-9:43 PM
2a. Why is (0,0) a good choice for a test point?
When could you not use (0,0)?
2b. For the graph , the boundary line is
the vertical line . Would you shade to
the left or rigt of the boundary? Explain.
Oct 6-9:46 PM
Solving Systems of Linear Inequalities
Solve the system of inequalities by graphing.
Check your answer.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
x
y
A. Graph
Boundary Line:
________________
x-int=____ y-int=_____
> so use a ________ line.
Shade ______ boundary line.
Oct 6-9:54 PM
B. Graph
Boundary Line:
________________
x-int=____ y-int=_____
so use a ________ line.
Shade ______ boundary line.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
x
y
The solutions are represented by the
_________ shaded regions.
Oct 6-9:03 PM
Ordered
Pair
In the
overlapping
shaded regions?
(0,0)
(2,3)
(-4,2)
(-2,4)
1a. How does testing specific ordered pairs tell you
that the solution you graphed is correct?
1b. Is (-2,2) a solution of the system of inequalities?
Why or Why not?
Oct 6-9:57 PM
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
x
y
Describe the solutions.
Graphing Systems of Inequalities
3
October 07, 2013
Oct 6-9:57 PM
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
x
y
Describe the solutions.
Oct 6-9:57 PM
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
x
y
Describe the solutions.
Oct 6-10:08 PM
2a. Is (1, -2) a solution to the system
2b. Is (3,2) a solution of the system
Oct 6-10:09 PM
2c. Can the solution of a system of inequalities
be a line? If so, give an example.
2d. Does the system and
have a solution? Explain.
Oct 6-10:13 PM
2e. Is it possible for a system of two linear
inequalities to have every point in the plane
as solutions? Why or why not?
Oct 6-10:15 PM