how do i find the points to graph these two linear sentences x+2y<=12 and 3x-y>=6? Please show all work.

- anonymous

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- amistre64

you graph the boundary lines:
x+2y = 12 and 3x-y = 6

- amistre64

pick a point not on the line; (0,0) is an easy testing point

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## More answers

- amistre64

and if those make the equation true; then the side with that point is good, shade it; if false, go with the other side

- anonymous

ah so you can start with any natural number then and plug it into the formula? or no?

- anonymous

equation*

- amistre64

you can, but it helps to see that these are line equations; and you just need 2 points to draw a line with right?

- amistre64

the lines themselves are boundaries for the inequalities; so graph them first;

- amistre64

x+2y = 12 and 3x-y = 6; graph these lines so you establish the boundaries for the inequalitites

- amistre64

then pick a point that is NOT on the line to test for a result. that point will be on one side or the other of the line right? The most conviennt point to test is the origin: (0,0)
x+2y<=12 and 3x-y>=6
0+2(0)<=12 and 3(0)-(0)>=6
0 <= 12 and 0 >=6
true false

- amistre64

all the points that make a true stament get shaded; all th epoints that make it false... shade the other side of the line

- anonymous

okay i get it use typing it out really help me... :D

- anonymous

lol you* typing it out...

- amistre64

school comp is slow lol

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- anonymous

its so weird maybe im asking the wrong question because my book is giving me 2 lines not one for the answer

- amistre64

the answer has 2 lines; I just demonstrated with 1

- anonymous

o sorry i get it now. i was confused for a second so then i can use the same points (0,0) for the second variable correct?

- amistre64

more like this
yes, as long as (0,0)aint on the line your testing, its the easiest one to use

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- amistre64

it is the common area that the two have that are solutions

- anonymous

gd i still am confused so now that we have that one line how do we plot the other line? because in the above answer you plug (0,0) into both variables

- anonymous

lemme just write this out and see if i can figure it out before i frustrate you.

- amistre64

you really make 2 solution sets and where they overlap, is the area I shaded

- anonymous

how do i give you a good review?

- amistre64

you might have to hit f5 to refresh your browser and youll see a 'good answer' button next to my name

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- anonymous

know a good free graphing programing?

- anonymous

program*

- amistre64

hmmm.... i use wolframalpha.com alot ; but it suits me

- amistre64

http://www.wolframalpha.com/input/?i=3x-y%3E%3D6+and++x%2B2y%3C%3D12

- anonymous

tyvm

- amistre64

youre welcome :)

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