Question

Graph the solution set of the system of inequalities or indicate that the system has no solution.

y ≥ 2x – 4
x + 2y ≤ 7
y ≥ -2
x ≤ 1

Answer 1

@Directrix Help me Please

Answer 2

@Yacoub1993 Is the task to graph the solution set of all four of the inequalities posted in the problem?

Answer 3

I dont know what to do
could you help me out with it

Answer 4

I asked you above if all four inequalities are drawn on one set of axes? It looks that way. In other words, this is not 4 separate problems.

Answer 5

At the moment, I am looking for a point that makes all 4 inequalities true and then we will look at options to see if that point is shaded.

We may have to draw the graphs. We'll see.

Answer 6

@Yacoub1993 Are you ready to work with me?

Answer 7

yes i am ready

Answer 8

(-2,0) is a point I found that satisfies all four of the inequalities given.

That means that (-2,0) should be part of the shaded region of the correct option.

Answer 9

Click on the first option.

Find the point (-2,0) on the graph of the first option.

Is the point (-2,0) shaded in that first option?

Or, is the point (-2,0) out in the white background?

Tell me what you think while I look at it, too.

Answer 10

ok wait

Answer 11

the second one right

Answer 12

the shaded one

Answer 13

Look at the first option.

I have attached the kind of thing we are doing so that you can understand.

Don't look at the second option yet.

Look at the attachment.

Answer 14

I located the point (-2, 0) in the first option, marked it, and noticed that it was not in the shade. So, option one is not the correct answer.

Answer 15

yes option one is not shaded

Answer 16

The reason we are using the point (-2,0) is that is makes all four of the given inequalities true.

y ≥ 2x – 4
x + 2y ≤ 7
y ≥ -2
x ≤ 1

Answer 17

So, now look at option 2 and find the point (-2,0) and see if it is shaded.

Please do not look at option 3 yet. :)

Answer 18

yes option 2
is shaded

Answer 19

Yes. So, option 2 is a contender but it could still be the *wrong option*. We have to test another point. So put option 2 on hold.

Let's go to option 3 and see if we can eliminate it from the running.

Answer 20

Option 1 is out. Option 2 is still in the running.

Now, test option 3.

Answer 21

What did you get for option 3?

Answer 22

@Yacoub1993 ^^^^

Answer 23

We're down to option 2 or option 3 as being correct.

Answer 24

option 3 is also shaded.... sory for late reply

Answer 25

And, 4 is not.

Answer 26

option 4 is not shaded so that one is also out

its between option2 and option3

Answer 27

To decide between options 2 and 3, we will test the point (-8,7).

That point makes all 4 inequalities true so it should be shaded.

This won't be so tedious. :)

Look for (-8,7) to see if it is shaded on option 2 and then option 3.

Answer 28

i am sure it will be C

Answer 29

i am sure it will be the third

Answer 30

Me, too. These inequalities are so tedious. But, we did it.

Answer 31

thnxs @Directrix

Answer 32

You are welcome.