Question

Which point is in the solution set for y < x+2? Explain your answer.

A. (-2, 0) because when you graph y < x+2, it is the x-intercept of the boundary line.

B. (1, 4) because when you graph y < x+2, it is a point that lies above the boundary line.

C. (2, 1) because when you graph y < x+2, it is a point that lies below the boundary line.

D. (0, 2) because when you graph y < x+2, it is a point on the boundary line.

Answer 1

@Vocaloid

Answer 2

any attempts so far? try plugging in the coordinates into y < x + 2 to see which one is true

Answer 3

the answer is A or C

Answer 4

if you plug in (-2,0) into the equation y < x + 2 is it true or false?

Answer 5

true

Answer 6

(-2,0) means x = -2 and y = 0

0 < -2 + 2

is this true or false?

Answer 7

sorry false my mistake

Answer 8

good so it can't be A

C is the only one that works

Answer 9

A system of inequalities is shown:

y ≤ x + 6

y ≥ 9x − 9

Which point is in the solution set of the system of inequalities shown? Explain your answer.

A. (3, 2) because it lies above the boundary line y=9x−9.


B. (-2, 2) because it lies above the boundary line y=9x−9 and below the boundary line y=x+6.


C. (3, 10) because it lies below the boundary line y=9x−9 and above the boundary line y=x+6.


D. (-1, 7) because it lies below the boundary line y=x+6.

Answer 10

try plugging in each answer choice and see which one makes both inequalities true

Answer 11

the answer is C

Answer 12

if you plug in (3,10) into y ≥ 9x − 9 is the inequality true or false?

Answer 13

false

Answer 14

good so the answer is not C, keep trying with the other choices

Answer 15

now it's either B or D

Answer 16

a OR c fit it

Answer 17

we have just concluded that it is not C

please do the calculations and see which answer choice makes the inequality true.

Answer 18

B if i'm not mistaken

Answer 19

good, B

Answer 20

A point (x, y) is the solution for the inequality y ≥ 2x + 1.

Which ordered pair has a y value that is less than or equal to 1 and satisfies the inequality shown?

A. (3, 8)


B. (1, 1)


C. (0, 1)


D. (2, 3)

Answer 21

the correct answer will satisfy two conditions:

1. the y-coordinate is less than or equal to 1
and
2. y ≥ 2x + 1 will be true

which answer choice satisfies both conditions?

Answer 22

D.

Answer 23

notice how for point (2,3) the y- coordinate is 3 which is greater than 1 so this cannot be our solution.

Answer 24

B

Answer 25

when you plug in (1,1) into y ≥ 2x + 1 is the inequality true or false?

Answer 26

FALSE

Answer 27

good so B cannot be the solution either

Answer 28

C

Answer 29

well done

Answer 30

(x, y) is the point of intersection of the boundary lines of the system of inequalities:

y ≥ −3x + 5

y ≤ x + 1

Select the graph that represents a system of inequalities that includes the same point of intersection (x, y) in its solution set.

A. https://d3upxwx9bggvi1.cloudfront.net/img/questions/arei12_1_222a.png

B. https://d3upxwx9bggvi1.cloudfront.net/img/questions/arei12_1_222d.png

C. https://d3upxwx9bggvi1.cloudfront.net/img/questions/arei12_1_222b.png

D. https://d3upxwx9bggvi1.cloudfront.net/img/questions/arei12_1_222c.png

Answer 31

I don't know if you would see it

Answer 32

hm. none of these graphs look right based on the equation, are those equations correct? :S

Answer 33

YES it's just in black form i don't know why they're like that

Answer 34

oh I think I know what they want you to do now

ok, so let's solve

y ≥ −3x + 5

y ≤ x + 1

for the point of intersection

Answer 35

cause when i solved it, i didn't look right with the equations

Answer 36

LIKE THEY DON'T MATCH

Answer 37

since they're both equal to y you can set -3x + 5 = x + 1 and solve for x

Answer 38

x = 1

Answer 39

good, now we plug x into one of the y-equations

y = x + 1 which means y = 1 + 1 = 2

so (1,2) is the solution

now look at each of the four graphs to see which one contains (1,2) within either the red or the blue regions

Answer 40

the answer is C

Answer 41

so C isn't quite it, keep trying with the other graphs

Answer 42

A

Answer 43

notice how the point (1,2) is not inside either the blue or red regions

make sure the point (1,2) is inside the blue or red regions, that is a requirement to be the solultion

Answer 44

ok D

Answer 45

good

Answer 46

The graph shown represents a system of inequalities.

https://d3upxwx9bggvi1.cloudfront.net/img/questions/arei12_1_245.png

Which system of inequalities is represented by the graph shown?


A. y > 2x − 5

y > −7x + 2


B. y < 2x − 5

y < −7x + 2


C. y < 2x − 5

y > −7x + 2


D. y > 2x − 5

y < −7x + 2

Answer 47

first check the graph and look at the red line

pretend it's just a regular line not a dotted line, what would be the equation in y = mx + b form for the red line?

Answer 48

the answer i chose is D

Answer 49

well done

Answer 50

THANK YOU FOR ALL YOUR HELP, I ALWAYS APPRECIATE IT