Question

Systems of Linear Inequalities

Determine whether the ordered pair is a solution of the given system.
A) (2.12);
y>2x +4
y<3x +7

Solve each system of inequalities by graphing.
B) y < 2x +4
-3x - 2y (greater than or equal too) 6

Answer 1

Also remember to tag?
@PeterPan ^.^
@TheKylieeM

There's a way to determine A... just replace x with 2, and replace y with 12.

Answer 2

Okay @PeterPan

Answer 3

So, in both inequalities,
y>2x+4
y<3x+7

Replace x with 2
and y with 12

See if it fits :)

Answer 4

So @PeterPan the first one would be y>2(2)+4? then multiply the 2(2)?

Answer 5

Don't forget to replace y with 12 :)

Answer 6

Yes I know I just did that one which I got y<36 + 7 so my answer for both would be

y>8
y<43

Answer 7

@PeterPan right?

Answer 8

y<43
?
How did you get? >.>

Answer 9

I added the 7 and the 36 I got from y<3(12) + 7

Answer 10

because 3(12) is 36... i think.

Answer 11

but that was an x :/
Why did you replace it with 12?
I said replace x with 2
replace y with 12

Careful next time, okay? ^.^

Answer 12

Oh! Okay! Hold on! Again! lol

Answer 13

Okay @PeterPan now I got for answers:

12>8 &&
12 <10

so the first one should be the solution for the given set.

Answer 14

12 < 10
?

Redo :)

Answer 15

yes. because 3(2) is 6 and 6 + 4 = 10

Answer 16

oh wait! I remember now!

Answer 17

But it was
y<3x +7
not
y<3x +2

Answer 18

oh I accidently put 4! instead of 7!

Answer 19

so then is would be 12<13 @PeterPan

Answer 20

Yeah, much better :)
So...
is
12 > 8
true?

Answer 21

Yes that is true!

So yes the ordered pair is a solution for equation A

Answer 22

YES it is a solution for the FIRST INEQUALITY, but is it a solution for the second inequality?
Is
12 < 13
true?

Answer 23

Yes it is because 13 is greater than 12! :)

Answer 24

and 12 is less than 13! :)

Answer 25

Then, it's settled.
(2,12) is a solution of the system :)

Answer 26

Whoo hoo! Next question! :D

Answer 27

hmmm... this is gonna be a tricky one :)
Can you graph lines?

Answer 28

Yes I can but I did look at this equation and I am VERY confused on how to graph something like this....

Answer 29

Yes, don't worry :)
First, pretend they're lines, and graph them...
y = 2x +4
-3x - 2y = 6

Answer 30

I'm still confused on how to graph lines like that... :|

Answer 31

@PeterPan

Answer 32

Hmm... first put them in this form:
y = mx + b

Answer 33

and how do I do that exactly? Also what do each letter stand for?

Answer 34

@PeterPan keep forgetting to tag you! ooops lol

Answer 35

Only tag me once. What I want you to do is rearrange the equation so that y stands alone on one side of the equation :)

Answer 36

like 2y - (-3x) (greater than or equal too) 6?

Answer 37

and y is already standing alone on the first equation

Answer 38

forget that they are inqualities, for now.
-3x - 2y = 6

Answer 39

okay but could it also be like the one I just gave but

2y - (-3x) = 6?

Answer 40

No... because
2y - (-3x) = 2y+3x
which isn't the same as -2y - 3x

Answer 41

but you just flip the inequality sign right? dont you have to do that when theres a negative?

Answer 42

Yeah, sure, but you sure failed to negate the right side (6)

Answer 43

negate?

Answer 44

make negative.

Answer 45

Oh! ...................................

Answer 46

so then how can i be able to make the y stand alone? I am really confused... o.0

Answer 47

Hang on...

Answer 48

Alright

Answer 49

Here, an example :)
\[\Large ax + by = c\]to isolate y, we bring all those without y to the right-side
\[\Large by=-ax+c\]Then divide everything by b, the coefficient of y...
\[\Large y = \frac{-ax+c}{b}\]That's how to isolate y :)

Answer 50

Okay so to get why by its self I have to divide -3x - 2 by 6??

Answer 51

y***

Answer 52

No...

Answer 53

grrrrrrrrrrrrr......................

Answer 54

Let's do it slowly :)
\[-3x-2y=6\]Let's bring x to the right side
\[-2y=3x+6\]

Answer 55

Oh! I thought that the 2 had to be on the same side as the 3

Answer 56

Not really, as long as you can get the y alone on one side, it should work :)

Answer 57

okay so next step?

Answer 58

Well, on the left side, it still says -2y, so we better divide everything by -2, to get rid of that coefficient, we get
\[\Large y = \frac{3x-6}{-2}\]And there you go, y is alone on one side :)

Answer 59

Oh! okay! so then?

Answer 60

Well, simplify...
\[\Large y = -\frac32x+3\]

Answer 61

I'm going to graph this line, and you do the other, okay?

Answer 62

okay

Answer 63

The coordinate system :)

Answer 64

okay

Answer 65

brb!

Answer 66

The way to graph a line is to get its intercepts. Its y-intercepts and x-intercepts.
Its x-intercept is obtained by letting y = 0, indeed, you can check this, if y = 0, then x = 2
So its x-intercept is the point (2,0)