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

- anonymous

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

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- chestercat

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- anonymous

##### 1 Attachment

- anonymous

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.

- anonymous

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

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## More answers

- anonymous

@satellite73

- anonymous

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

- anonymous

Thx!!! ;)

- anonymous

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

- anonymous

Yes

- anonymous

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

- anonymous

Ok

- anonymous

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

- anonymous

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

- anonymous

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?

- anonymous

1

- anonymous

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

- anonymous

what is the smallest y value?

- anonymous

-3

- anonymous

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

- anonymous

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

- anonymous

Oh, ok. No worries.

- anonymous

we are just making a box around them

- anonymous

Oh

- anonymous

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

- anonymous

Ok

- anonymous

all of those points are in that box

- anonymous

So, is this the system of inequalities?

- jim_thompson5910

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

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- anonymous

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

- anonymous

Kk

- anonymous

you could probably be fancier and come up with three inequalities instead of 4, |dw:1450322440841:dw|

- anonymous

but why bother?

- anonymous

Right

- anonymous

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

- anonymous

Ok, what's next?

- anonymous

have a snack?

- anonymous

Haha

- jim_thompson5910

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

- anonymous

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

- anonymous

Ok, thx for everything already

- jim_thompson5910

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

- anonymous

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!!!

- jim_thompson5910

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

- jim_thompson5910

here's what I'm referring to
http://assets.openstudy.com/updates/attachments/567224fbe4b0d5f07925328b-jim_thompson5910-1450322371474-system_of_inequalities2.jpg

- jim_thompson5910

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

- anonymous

???

- jim_thompson5910

where are you stuck?

- anonymous

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! :(

- jim_thompson5910

well we can work together to get to the answers

- anonymous

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

- jim_thompson5910

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.

- anonymous

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?

- jim_thompson5910

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 \(\Large x \ge 2\)

- anonymous

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:

- jim_thompson5910

well the pictures help you build up the system I wrote above, which was
\[\Large \begin{cases}x \ge 2\\y \ge -4\end{cases}\]

- jim_thompson5910

scroll up to see my explanation how I got that

- anonymous

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

- jim_thompson5910

points B and C, yes

- jim_thompson5910

as shown in the purple region

- anonymous

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?

- jim_thompson5910

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

- jim_thompson5910

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

- jim_thompson5910

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

- anonymous

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

- jim_thompson5910

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

- jim_thompson5910

yes say how B and C are in the purple region

- anonymous

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

- jim_thompson5910

so my drawing is completely confusing?

- anonymous

No, I'm just confused

- anonymous

Hello?

- jim_thompson5910

please be more specific where you're stuck

- jim_thompson5910

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

- jim_thompson5910

and how each inequality is graphed (from that system)

- anonymous

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

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