Question

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

(1, 0)

(-5, -2)

(0, -3)

(-1, 5)

Answer 1

please help me

Answer 2

the easiest way is to plug the values of the given points.

Answer 3

for example, plug (1, 0) :
the first one gives 0 < 2 +4 so 0 < 6 this is true
the second one gives: 0 < -2 + 2 so 0 < 0 this is false
so this point is not the answer.

Answer 4

so which is the asnwer

Answer 5

now try and plug the other points and see

Answer 6

i still didnt get the answer

Answer 7

show me how you plug the second point for example

Answer 8

no i mean i dont
understand

Answer 9

so again, for the first point (1,0)
this point means x=1 and y=0
now you have two inequalities to satisfy
A. y < 2x + 4
B. y < -2x + 2
if you substitute x =1 and y = 0 in A
you get
0 < 2*1 + 4
0 < 6
this is true.

but, if you subtitute x =1 and y = 0 in B
you get
0 < -2 + 2
0 < 0
this is false.

so this point doesnt satisfy both inequalities.

Answer 10

still dont get it

Answer 11

you dont even try :(

Answer 12

show me how you do it with the second point

Answer 13

another way to solve this problem is by graphing both inequalities.

Answer 14

i graphed it

Answer 15

good.
now which of the points is in the dark area ?

Answer 16

?

Answer 17

(0,-3)