Question

Which of the following points lie in the solution set to the following system of inequalities?

y < -3x + 3
y < x + 2

(1, -5)

(1, 5)

(5, 1)

(-1, 5)

Answer 1

@halorazer
@mihirb
anyone.

Answer 2

@ganeshie8

Answer 3

@wolf1728

Answer 4

@31356

Answer 5

@jim_thompson5910

Answer 6

let's randomly pick an answer choice, say choice C which is the point (5, 1) and plug that point into both inequalities

Answer 7

for the first inequality, we get

y < -3x + 3

1 < -3(5) + 3

1 < -15 + 3

1 < -12

is that last inequality true?

Answer 8

no its not true.

Answer 9

so choice C is NOT the answer. The (x,y) pairing must satisfy both inequalities (ie make them true)

Answer 10

Let's try choice D

Answer 11

@Official_Hotboy its not C

Answer 12

plug in (x,y) = (-1, 5)

we'll start with inequality #1

y < -3x + 3

5 < -3(-1) + 3

5 < 3 + 3

5 < 6 ... is this true?

Answer 13

yes its true.

Answer 14

ok now test the other inequality

Answer 15

plug (x,y) = (-1, 5) into y < x + 2 and tell me what you get

Answer 16

and tell me if that is true or not

Answer 17

itd be -5<0 and its true.

Answer 18

i didnt do a negative one

Answer 19

i did 1, -5

Answer 20

y < x + 2

5 < -1 + 2 ... plug in (x,y) = (-1,5)

5 < 1 ... is that true?

Answer 21

thats not true.

Answer 22

ok so D is out because it doesn't make the second inequality true

Answer 23

-1, 5 is d and we just did that one already im confused.

Answer 24

we have to test BOTH inequalities (not just one)

Answer 25

if one inequality is false, then you move on

Answer 26

oh.

Answer 27

when I encountered a false statement, I knew the other inequality didn't matter because it has to make them both true

Answer 28

so what answers do we have left.

Answer 29

but when you encounter a true statement, you have to make sure the other one is true too

Answer 30

do you see how I eliminated choice C?

Answer 31

and we just eliminated choice d to.

Answer 32

so its either a or b

Answer 33

the first part of D is true, but the second is false, so that leads to D being eliminated too

Answer 34

exactly so we either have a or b left.

Answer 35

so test those points and tell me what you get

Answer 36

there both true.
i did answer a and for the first point i got -5<0 and the second i got -5<3

Answer 37

both true.

Answer 38

so a is correct.

Answer 39

good, now test choice B (just for practice)

Answer 40

for the first point it was already wrong so i already know its wrong.

Answer 41

so when you plugged in (1,5) into y < -3x + 3, what final inequality did you get?