Question

Which point lies in the solution set for the following system of inequalities?
y > x + 4
y > -2x + 2

(-4, 0)

(-3, 2)

(2, -1)

(0, 6)

Answer 1

all you do here is plug each answer choice into each inequality

if a particular answer choice makes BOTH inequalities true, then that answer choice is in the solution set

Answer 2

so for instance, choice A is (-4,0)

plug it into y > x + 4 to get

y > x + 4

0 > -4 + 4

0 > 0

but that's false, so (-4,0) is NOT in the solution set for y > x + 4

which means it's NOT in the overall solution set

so A is out

Answer 3

I think its c, may I be right?

Answer 4

let's find out

Answer 5

y > x + 4

-1 > 2 + 4 ... plug in (2,-1)

-1 > 6

is that true?

Answer 6

no

Answer 7

so C isn't the answer

Answer 8

D?

Answer 9

y > x + 4

6 > 0 + 4 ... plug in (0,6)

6 > 4

works, so far, so good

Answer 10

now let's check the other inequality

y > -2x + 2

6 > -2(0) + 2

6 > 0 + 2

6 > 2

that's also true

Answer 11

both inequalities are true for (0,6) so it is in the solution set

Answer 12

so its right :)

Answer 13

yep

Answer 14

D is correct

Answer 15

what about this?
-4x + 2y < 8
y < -x + 4

-4x + 2y > 8
y greater than or equal to -x + 4

-4x + 2y < 8
y > -x + 4

-4x + 2y > 8
y > -x + 4

Answer 16

hmm this may be a pain do to by hand, do you have geogebra?

Answer 17

no :(

Answer 18

are you able to download and install programs on the computer you are on?

Answer 19

nvm I'll just post the 4 graphs that geogebra produces

when you can, please download and install geogebra as it's a very useful graphing calculator program (that can do a number of things, including graphing inequalities)

Answer 20

okay I will definitely try and do that

Answer 21

ok one sec while I get the graphs

Answer 22

okay

Answer 23

here is graph a)

Answer 24

here is graph b)

Answer 25

here is graph c)

Answer 26

and here is d)

Answer 27

which two graphs are similar to the original one given?

Answer 28

D!

Answer 29

perfect

Answer 30

b is another possible choice...BUT...notice how it has a solid boundary line (when the two boundary lines should be dashed)

Answer 31

yes d looks exactly like the original

Answer 32

agreed (even if it's a bit small, not sure why though)

Answer 33

can I ask you for one more and ill be done?

Answer 34

sure

Answer 35

-x + 3y < 9
y > -2x + 1

-x + 3y less than or greater to 9
y > -2x + 1

-x + 3y < 9
y greater than or equal to -2x + 1

None of these systems represent the graph shown.

Answer 36

this is a lot like the previous one

Answer 37

the final solution set is the green solution set (where the two regions overlap)

Answer 38

so how do I solve to find them?

Answer 39

one sec

Answer 40

here's what geogebra spits out

Answer 41

graph a)

Answer 42

graph b)

Answer 43

graph c)

Answer 44

unfortunately they all shade the same basic region

BUT

the boundary lines are different (see if you can spot the differences)

Answer 45

B?

Answer 46

good

Answer 47

thank you so much:)

Answer 48

sure thing