Question

The coordinate plane below represents a city. Points A through F are schools in the city.

Part A: Using the graph above, create a system of inequalities that only contain points A and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.

Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A.

Answer 1

Part C: William can only attend a school in his designated zone. William's zone is defined by y < -x - 1. Explain how you can identify the schools that William is allowed to attend.

Answer 2

@Mlink1290 @Smileyside @geerky42 @Michele_Laino @robtobey @butterflydreamer @Calvin3 @mathstudent55 @mathislovemathislife @amistre64 @tylermcmullen23 @Ogziii @HackberryAbby18 @GTDoubleXPGaming @rishavraj @horsegirl27

Answer 3

Sorry, idk :/

Answer 4

Thats okay

Answer 5

@dan815 @ckellar2 @maddiegirl @Chiko_1278

Answer 6

Do you know the actual coordinates?

Answer 7

I have the graph, i can write out the coordinates if you want?

Answer 8

@HackberryAbby18

Answer 9

where are the overlapping shaded regions?

Answer 10

I think i'm supposed to find that out.

Answer 11

Yes what are the coordinates

Answer 12

A (2,-3)
B (-3,-4)
C (-4,2)
D (2,4)
E (3,1)
F (-2,3)
@HackberryAbby18

Answer 13

And which ones do u need most?

Answer 14

A and E

Answer 15

@HackberryAbby18

Answer 16

hint:
we can consider the subsequent lines:
y=x
and:
y=-3x

Answer 17

What about points A and E? i don't understand how that has to do with it :c

Answer 18

@Michele_Laino

Answer 19

@skittles_for_life6422 @freckles @Mlink1290 @rainbow_rocks03 @owllover123 @Legends @campbell_st @Catlover5925 @mathsciencehistory @aaronq @ajanijones @Ashleyisakitty @micahm @kels200105 @jeffyblood @sammixboo

Answer 20

Please help

Answer 21

part C in the picture is -4 , -2

Answer 22

For part C i need to explain how to find the answer. I really need help with part A right now though first :c

Answer 23

@HackberryAbby18

Answer 24

Somebody please help, iv been stuck on this for over an hour :c

Answer 25

@Tarantulagirl98

Answer 26

@dan815 @perl @nincompoop @Ashleyisakitty @Michele_Laino @HackberryAbby18

Answer 27

Still need help? Whole question?

Answer 28

omg yes thank you, please.

Answer 29

Part A: Using the graph above, create a system of inequalities that only contain points A and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.

Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A.

Lets take Part A first :D

Answer 30

okay c:

Answer 31

Part A: Using the graph above, create a system of inequalities that only contain points A and E in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above.

Any ideas?

Answer 32

Only that i need to find the coords for A and E, witch are
A (2,-3)
E (3,1)

Answer 33

idk past that

Answer 34

here, the shaded region is given by those points whose y-coordinate satisfy the subsequent condition:
\[\Large - 3x \leqslant y \leqslant x\]

Answer 35

Oh my @Michele_Laino ...
I woulda just have done:
y < 2x - 1

Answer 36

I believe @Michele_Laino has this atm :D
After all they might do the work and explain it better than a random 10th grader xD

Answer 37

y < 2x - 1 instead of -3x<y <x?

Answer 38

when x> 0 or x=0

Answer 39

okay @undeadknight26 ill tag you again if i need you if thats okay?
thanks for the help

Answer 40

Any time @AlexandervonHumboldt2
Btw welcome to Openstudy!

Answer 41

@Michele_Laino so does that take care of part A?

Answer 42

Well...I miss-tagged...
Thats quite embarrassing ._.

Answer 43

haha cx thats okay, and thank you c:

Answer 44

@Michele_Laino I have this for part A, does this look right to you?
A: (2,-3)
E: (3,1)
the shaded region is given by those points whose y-coordinate satisfy the subsequent condition -3x<y <x
Shade A and E within the lines y = x and y = -3x

Answer 45

yes! I think that your answer is right! @AllyBearxx

Answer 46

Great! thank you so much ^.^
could you help me with Part B now?

Answer 47

Part B: Explain how to verify that the points A and E are solutions to the system of inequalities created in Part A.

Answer 48

ok!

Answer 49

Awesome ^.^ thanks

Answer 50

we have to replace the coordinate of point A, into our inequality:
\[ - 3x \leqslant y \leqslant x\]

Answer 51

for example, for point A, we have:
\[\Large \begin{gathered}
- 3 \times 2 \leqslant - 3 \leqslant 2 \hfill \\
- 6 \leqslant - 3 \leqslant 2 \hfill \\
\end{gathered} \]
which inequality is true

Answer 52

I dont understand, how do i replace the coordinate of point A?

Answer 53

you have to rplace x with 2, and y with 3, into this inequality:
\[ - 3x \leqslant y \leqslant x\]

Answer 54

replace*

Answer 55

so -3x <3 <2?

Answer 56

oh wait or -3x <-3 <2?

Answer 57

no, it is:
-3*2 < -3 < 2

Answer 58

okay

Answer 59

and then what?

Answer 60

you have to do the same with point E

Answer 61

point E=(3,1)

Answer 62

okay so it would be 1*-3 <1 <-3?

Answer 63

it is:
-3*1< 1 < 3

Answer 64

oh okay

Answer 65

please wait:

Answer 66

it is:
-3*3 < 1 < 3

Answer 67

How did you get that?

Answer 68

since I have replaced x wiyh 3, and y with 1 into the subsequent inequality:
\[ - 3x \leqslant y \leqslant x\]

Answer 69

oops..with*

Answer 70

oh alright, so does that take care of part B?

Answer 71

This is what i have for part B: You have to replace the coordinate of point A, into the inequality -3x<y <x to get -3*2 < -3 < 2, and then replace the coordinate of point E to get -3*1< 1 < 3

Answer 72

yes! we have solved part B

Answer 73

that's right!

Answer 74

awesome :D
okay so would you help me with part C as well please?

Answer 75

ok!

Answer 76

thank you so much! c:

Answer 77

Part C: William can only attend a school in his designated zone. William's zone is defined by y < -x - 1. Explain how you can identify the schools that William is allowed to attend.

Answer 78

we have to draw the line whose equation is:
y=-x-1

Answer 79

okay so where would that be?

Answer 80

here is the drawing:

Answer 81

it passes through point A

Answer 82

yes!

Answer 83

So would he have to go to school A?

Answer 84

nevertheless the question asks to us, what are the points whose y-coordinate is less than -x-1

Answer 85

namely the points points that lie below the straight line y=-x-1

Answer 86

So thats point A?

Answer 87

no, since A belongs to the line y=-x-1

Answer 88

But William would have to go to school A since his zone "line" meets A?

Answer 89

or is his zone below Point A? and the school hed go to would be Point B or C