(-6, 5) (3, 2) (0, 4) (0,0) (1, -4) (2,4) - Rushing
5
Algebra I - Unit 6: Topic 2 – Systems of Inequalities -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 x y Student Notes – Systems of Inequalities pp 421-426 Remember: To graph a line you need a ____________________ and a _______________________________________. GRAPHING INEQUALITIES 1. Graph the linear inequalities 1 y x t and y x d Shade UP Shade DOWN Dotted Solid A solution of a system of inequalities is _______________________________ _______________________________ _______________________________ 2. Circle the ordered pairs that represent solutions to the system of inequalities to the left. (-6, 5) (3, 2) (0, 4) (0,0) (1, -4) (2,4) 3. Is (-3, 6) a solution of the system of inequalities 3 6 9 y x t and 6 3x y d ? 4. Is (1,3) a solution of the system of inequalities 4 1 y x ! and 6 3 y x t ? State which points are solutions to the system of inequalities we graphed. Yes or No A. (0, 0) __________ B. (2, 2) __________ C. (-1, 4) __________ D. (4, 1) __________ E. (-3.5, -1.5) __________
Transcript of (-6, 5) (3, 2) (0, 4) (0,0) (1, -4) (2,4) - Rushing
Algebra I - Unit 6: Topic 2 – Systems of Inequalities
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4-3-2-1
1234567
x
y
Student Notes – Systems of Inequalities pp 421-426 Remember: To graph a line you need a ____________________ and a _______________________________________.
GRAPHING INEQUALITIES 1. Graph the linear inequalities 1y xt � � and y xd Shade UP Shade DOWN
Dotted
Solid
A solution of a system of inequalities is _______________________________ _______________________________ _______________________________
2. Circle the ordered pairs that represent solutions to the system of inequalities to the left.
(-6, 5) (3, 2) (0, 4) (0,0) (1, -4) (2,4)
3. Is (-3, 6) a solution of the system of
inequalities 3 6 9y xt � � and 6 3x yd � ?
4. Is (1,3) a solution of the system of inequalities
4 1y x! � � and 6 3y x� t ?
State which points are solutions to the system of inequalities we graphed.
Yes or No
A. (0, 0) __________
B. (2, 2) __________
C. (-1, 4) __________
D. (4, 1) __________
E. (-3.5, -1.5) __________
Algebra I - Unit 6: Topic 2 – Systems of Inequalities
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4-3-2-1
1234567
x
y
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4-3-2-1
1234567
x
y
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4-3-2-1
1234567
x
y
Solve each by graphing, then name one point that lies in the solution area.
5. ��
11
yx
6. �� !3
8 4 12yx y
7. � !� d
2 2 61
x yy x
Algebra I - Unit 6: Topic 2 – Systems of Inequalities
-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
x
y
AB
C
D
Student Notes – Systems of Inequalities pp 421-426 Write a system of inequalities for the graphs below: 1. 2.
3. For which point on the grid satisfies the conditions 132
x d � and 1
52
y xt � ?
4. Jamal makes $12 an hour mowing yards and $6 an hour raking leaves. He cannot work more than 15 hours per week. Write and graph the two inequalities that Jamal can use to determine how many hours he needs to work at each job if he wants to earn at least $120 per week.
If Jamal decides to mow for 11 hours, what is the maximum number of hours he could rake? If Jamal decides to rake for 6 hours, what is the minimum number of hours he would need to mow?
Inequalities
__________________________
__________________________
A. Point A B. Point B C. Point C D. Point D
Inequalities
__________________________
__________________________
Let Let
-5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-3
-2
-1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
x
y
hours mowing
hours raking
Algebra I - Unit 6: Topic 2 – Systems of Inequalities
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4-3-2-1
1234567
x
y
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4-3-2-1
1234567
x
y
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4-3-2-1
1234567
x
y
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4-3-2-1
1234567
x
y
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7
-7-6-5-4-3-2-1
1234567
x
y
-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
-9-8-7-6-5-4-3-2-1
123456789
x
y
Practice – Systems of Inequalities pp 421-426 Name _________________________________ Date __________________ Period _______ 1. State which points are solutions to the system of inequalities graphed below. 2. Is (2, -3) a solution of the system of inequalities 8 2x yt � and 2 4 2y x� � � ? Solve each by graphing, then name one point that lies in the solution area. 3. 2y xt 4. 1y x� � 5. y x! 1x t � 2 1y xd � 3x y� t 6. 1y xt � 7. 2 6x y� ! � 8. 8x y� d 4 5 20x y� t 2 2 5x y� t 0x t 3y t
Yes or No
A. (0, 0) ___________
B. (-3, 0) ___________
C. (-1, -5) ___________
D. (1, -2) ___________
E. (-4, 3) ___________
F. (-4, 0) ___________
Algebra I - Unit 6: Topic 2 – Systems of Inequalities
-9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
x
y
A
B
C
D
-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
-7-6-5-4-3-2-1
123456789
101112131415161718192021
x
y
Practice – Systems of Inequalities Day 2 pp 421-426 Name _________________________________ Date __________________ Period _______ Write a system of inequalities for the graphs below. 1. 2.
3. For which point is 92
y t � and 175
x � � ?
4. Jessica is buying hats for everyone invited to her birthday. The Party Store is selling party hats for $2 each and crowns for $5 each. Jessica expects no more than 20 people.
A) Write and solve (by graphing) the system of inequalities to find out how many party hats, x, and crowns, y, Jessica can buy if she does not want to spend more than $60.
B) Is the ordered pair (-5, 10) a solution to this situation?
C) Is the ordered pair (2.5, 8.5) a solution to this situation?
D) If Jessica decides to buy 9 party hats, what is the maximum number of crowns she can buy? E) If Jessica decides to buy 6 crowns, what is the minimum and
maximum number of party hats she can buy?
Inequalities
_________________________ _________________________
Inequalities
_________________________ _________________________
A. Point A B. Point B C. Point C D. Point D
