Question

Question:
https://snag.gy/l3FyZi.jpg
Kinda confused @mathmate

Answer 1

How does this work?

Answer 2

The short-cut for the other problem still works, but for x this time.
You see that the area is to the right of x, this means that all points in the shaded area is greater than those ON the line.
So you look for the choice where x is positioned on the "big" side of the equal sign.
For example, for the first choice,
first equation: x is on the smaller side of the inequality sign, (no good)
second equation: x is on greater side of the inequality sign, (good)
So overall, first choice does not work (for both equations).
Keep on doing this and you'll find the right on.


Note:
This is a short cut method for simple questions like this.
You will still NEED to learn to match equations with graphs.

Answer 3

I am really confused Sorry D:

Answer 4

Well, there is still another shortcut that works in all cases.
Choose a point in the region, say (0,0) i,e, origin.
Substitute x=0, y=0 in each equation to see if the equation is satisfied.
If both equations of a particular choice are satisfied, then the choice represents the region.

Are you following?

Answer 5

I think so,

Answer 6

Ok, i'll test the first choice as an example:
we have
y\(\ge\)x+8 test with (0,0)
If we put x=0, y=0, then the equation becomes
0\(\ge\)0+8, or
0\(\ge\)8 is this valid?

Answer 7

No its not

Answer 8

If any one equation in a choice is not valid, that choice is also not valid.
So proceed to the next choice.
I'd like you to test the other three choices until you get one that has both equations valid when substituted with (0,0).

Answer 9

You can show me all the work, or just the one that works.

Answer 10

@MellamoKatie
How many have you checked so far?

Answer 11

Well I had to switch computers can you give me a momment?

Answer 12

Okay so for B I got y <= x+3
0<=3
C. 0>=8
D. 0<=8
@mathmate

Answer 13

Good work!
The choice that has \(both\) equations valid is your answer.

B 0<=3 valid, so it depends on the second equation
C. 0>=8 not valid, so C is not your choice
D. 0<=8 valid, so it depends on the second equation

You're almost there!

Answer 14

Thanks so much!!!!!

Answer 15

So all you need to check will be the second equation of B & D. They both have the first one valid. You just need the choice that has the second equation also valid.

Answer 16

Wait so is it D? Or is it B?

Answer 17

@mathmate

Answer 18

Ohhhh the second equation!!! I see one second!

Answer 19

Okay so for B I got 0 <= -8
D. 0 >= -8

Answer 20

@mathmate

Answer 21

0>=-8 is valid, but
0<=-8 is not.
So you can now make a choice.

Answer 22

Yeah because -8 is less than 0

Answer 23

So its D thank you so much!

Answer 24

Exactly! Well done! :)
You're welcome!

Answer 25

:DDDD