Question

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

Answer 1

Part A: Using the graph above, create a system of inequalities that only contain points B and C 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 B and C are solutions to the system of inequalities created in Part A.

Part C: Lisa can only attend a school in her designated zone. Lisa's zone is defined by
y > 2x + 5. Explain how you can identify the schools that Lisa is allowed to attend.

Answer 2

PLEASE HELP A.S.A.P. I WILL GIVE A MEDAL IF YOU EXPLAIN THE MATERIAL WELL. THX!!! ;D

Answer 3

@satellite73

Answer 4

we can do this, it is a pain but we can do it

Answer 5

Thx!!! ;)

Answer 6

i am not really clear on the wording, but is is clear that the x coordinates of both B and C are 3 right?

Answer 7

Yes

Answer 8

so since they are both 3, they are certainly both bigger than say \(2\) so maybe you can use \(x>2\) as one inequality since all the other points have smaller x values

Answer 9

Ok

Answer 10

but i think you need more since it says a "system"

Answer 11

True, I think we should also do f and c, they have the same y-int.

Answer 12

ok so we know they are both to the right of 2, so \(x>2\) what is the largest y value for those two points?

Answer 13

1

Answer 14

ok so both of them have \(y<1\) we can use that one

Answer 15

what is the smallest y value?

Answer 16

-3

Answer 17

ooops i made a mistake, i meant \(y<2\) since \(1<2\)

Answer 18

ok so another we can use is \(y>-4\)

Answer 19

Oh, ok. No worries.

Answer 20

we are just making a box around them

Answer 21

Oh

Answer 22

and maybe we close it in with \(x<4\)

Answer 23

Ok

Answer 24

all of those points are in that box

Answer 25

So, is this the system of inequalities?

Answer 26

here is one of infinitely many ways to do this (see attached)

notice how the blue and red regions overlap to form the purple region

Answer 27

i made a mistake there
\[x>2,x<4,y>-4,y<2\] will do it

Answer 28

Kk

Answer 29

you could probably be fancier and come up with three inequalities instead of 4,

Answer 30

but why bother?

Answer 31

Right

Answer 32

we get something that looks like this, a reactagle around the points
actually @jim_thompson5910 picture is better
http://www.wolframalpha.com/input/?i=x%3E1+and+x%3C4+and+y%3E-4+and+y%3C2

Answer 33

Ok, what's next?

Answer 34

have a snack?

Answer 35

Haha

Answer 36

whatever you got for part A, verify it in part B

Answer 37

actually what is next is @jim_thompson5910 s help since i really have to go to bed
but i am sure you can do it

Answer 38

Ok, thx for everything already

Answer 39

There are infinitely many ways to do this, but the easiest is to probably just use two inequalities like I've shown. It's up to you how you answer part A

Answer 40

I know it's kind of against Open Study's policy, but since you already explained half to me. Do you think you could write down all the answers? You seem to know what you're doing, and I need to go to bed too. Please!!!

Answer 41

the red region is the solution set to \(\Large x \ge 2\)

the blue region is the solution set to \(\Large y \ge -4\)

so the purple region is the solution set to this system

\[\Large \begin{cases}x \ge 2\\y \ge -4\end{cases}\]

Answer 42

here's what I'm referring to

http://assets.openstudy.com/updates/attachments/567224fbe4b0d5f07925328b-jim_thompson5910-1450322371474-system_of_inequalities2.jpg

Answer 43

part A has you set up some system

part B wants you to prove how points B and C are solutions to that system, ie how they are in the solution set. You need to plug the coordinates of each point into the inequalities

Answer 44

???

Answer 45

where are you stuck?

Answer 46

I know a lot of people do things like this to get out of doing work, but I really do work, and I'm not trying to use you, but could you please write the answers. I have school at 7 am. I really can't take this long. I've been on this question since 8 pm. I swear I'm not exaggerating. Then after a long while I decided to try to get help because my parents didn't understand it and couldn't explain and I HAVE to go to bed. Please, believe me, I really need the answers! :(

Answer 47

well we can work together to get to the answers

Answer 48

Thx, but pls make it quick!!! Like maybe 2 min.

Answer 49

Idk if that's enough time, but I need to know where you're stuck. Do you understand what I've explained so far? It's ok if you didn't. Let me know where you got stuck.

Answer 50

I just don't know what to submit for part a, I understand what we did, but don't know how that answers the question, and when I submit it what exactly should I write?

Answer 51

look at this

http://assets.openstudy.com/updates/attachments/567224fbe4b0d5f07925328b-jim_thompson5910-1450322371474-system_of_inequalities2.jpg

hopefully you see how I got the red region to be the inequality \(\Large x \ge 2\)

Answer 52

I understand that, but what exactly should I type, we can't submit pictures and files. I can only type the answer. Would it be:

Answer 53

well the pictures help you build up the system I wrote above, which was

\[\Large \begin{cases}x \ge 2\\y \ge -4\end{cases}\]

Answer 54

scroll up to see my explanation how I got that

Answer 55

That is the system of inequalities only for b and c, right?

Answer 56

points B and C, yes

Answer 57

as shown in the purple region

Answer 58

Ok, now how would I explain in words how the lines were groaned and shaded. Would I just say that if you use the substitution method you can graph your answer and shade where it says and the lien would be solid?

Answer 59

for x >= 2, it's a vertical line through 2 on the x axis

then you shade to the right of that vertical line. That forms the red region

Answer 60

for y >= -4, it's a horizontal line through -4 on the y axis

then you shade above the horizontal line. That forms the blue region

Answer 61

combine the two regions, they overlap to form the purple region

Answer 62

But it's only asking for b and c, so should I only describe those?

Answer 63

it all builds up to form the purple rectangle you see on the attachment

Answer 64

yes say how B and C are in the purple region

Answer 65

Ok, i thought I understood, but now I'm totally confused

Answer 66

so my drawing is completely confusing?

Answer 67

No, I'm just confused

Answer 68

Hello?

Answer 69

please be more specific where you're stuck

Answer 70

all they want for part A is the system of inequalities really

Answer 71

and how each inequality is graphed (from that system)

Answer 72

I just don't know, everything is confusing! I should probably just guess and fail, I'm not aloud up this late. Anyways, thx for trying