Question

Solve the system by graphing.

Answer 1

do you have geogebra?

Answer 2

geogebra is a tool to help graph equations

Answer 3

http://www.geogebra.org/cms/

Answer 4

are you able to download that?

Answer 5

I'll try it just a sec

Answer 6

ok

Answer 7

ok when it's done, install it and let me know when that's done

Answer 8

ok open it up

Answer 9

you should see an xy axis

Answer 10

ok

Answer 11

at the bottom, do you see "input" then a place where you can type stuff in?

Answer 12

yeah i think so

Answer 13

ok type in the equations one at a time and hit enter

or

paste in each equation one at a time and hit enter

Answer 14

each time you hit enter, the corresponding line will come up

Answer 15

you should see the two lines intersecting at a point

but that point is NOT (1,3)

Answer 16

were you able to graph the two lines?

Answer 17

yes it looked exactly like my graph in the options

Answer 18

if so, then go to file ---> save as and save the file with any name you want

save it in a spot where you can find it (eg: the desktop)

then send that file to me so I can have a look

Answer 19

thanks

Answer 20

very good, I'm getting the same

Answer 21

so you just mixed up your x and y values

Answer 22

and yes, it's (3,1)

Answer 23

ah thank you!

Answer 24

sure thing

Answer 25

Do you know how to solve a problem like that using a table

Answer 26

what do you mean

Answer 27

oh you mean instead of graph, you use a table?

Answer 28

well the solution to the system is when x and y are the same value and they satisfy both equations (ie they make them true)

Answer 29

yes instead of a graph

Answer 30

are you given the tables for both equations?

Answer 31

I don't know that upload is all i have

Answer 32

ok you'll have to make your own table then

Answer 33

do you know how to do this?

Answer 34

not really

Answer 35

ok luckily you can use geogebra to generate the tables as well...but we first need to solve for y

Answer 36

so what do you get when you solve each equation for y?

Answer 37

okay so we have to isolate the variables?

Answer 38

not sure

Answer 39

you just isolate y in each case

Answer 40

so for instance

3y = 4x + 7

y = 4x/3 + 7/3

y = (4/3)*x + 7/3

Answer 41

now solve the other equation for y

Answer 42

y=-x+28/4?

Answer 43

Is the answer (-4,-3)

Answer 44

close

Answer 45

remember that 4 should be negative giving you

y = -x - 7

Answer 46

you graphed it didn't you? lol

Answer 47

yes i did

Answer 48

that's ok, that's what I would have done

Answer 49

but did you want to use the table?

Answer 50

so is that right?

Answer 51

(-4,-3) is the answer

Answer 52

but did you want to see why it is with a table?

Answer 53

Yeah i diddn't understand that part

Answer 54

ok go up to the menu where you see "file, edit, etc" and click on "perspectives"

then click "spreadsheet & graphics"

Answer 55

that will bring up a table or grid like you would see in excel

Answer 56

the good news is that if you know how to work excel, then this is very similar in geogebra

if not, then it's not too hard to learn

Answer 57

tell me when you get there

Answer 58

Hold on I'm looking for perspectives

Answer 59

ok its up at the top

Answer 60

okay i have the psread sheet up what now?

Answer 61

ok in cell A1, which is in the upper left most portion of the table, type in -10

then under that in cell A2, type -9

Answer 62

then select both cells by clicking and dragging the mouse over them

after that, grab that square dot you see in the bottom right corner of your selection and drag it as far as you can down

Answer 63

doing that will generate the values -10, -9, -8, -7, -6, ... up to a certain stopping point

Answer 64

do you see what I'm referring to?

Answer 65

no I want you to generate -10, -9, -8, -7, -6, ... etc until you reach a certain stopping point

you can do it manually (which is a pain)

or you can use the trick I'm describing above

Answer 66

btw these are the x values for the table

Answer 67

no everything so far is in column A

Answer 68

okay one sec

Answer 69

ok

Answer 70

ok i have negative 10 thru -1 down cell A what do i do next

Answer 71

ok those are your x values

Answer 72

now we're going to generate the y values for the first equation y = (4/3)*x + 7/3

we do this by going up to cell B1 and typing exactly what you see below

= (4/3)*(A1) + 7/3

and hitting enter

Answer 73

once you do that, you should see a number pop up

this is the y value if you plug in the x value that lives in cell A1

in other words...

the number that is in cell B1 is the y value when you plug x = -10 into y = (4/3)*x + 7/3

Answer 74

do you see a number pop up in cell B1

if so, what is that number?

Answer 75

-11

Answer 76

very good

Answer 77

now select that cell by clicking on it one time

then click and hold onto that square dot in the bottom left corner

drag it down until you reach the bottom level of column A

Answer 78

so you're basically generating a list of numbers in column B that is the same size as column A

Answer 79

okay what next

Answer 80

ok now move onto cell C1 and type this in

= -1*(A1) - 7

Answer 81

hit enter

then grab the square dot and drag it down to make another list of values in column C (that's the same size as A and B)

Answer 82

okay what now

Answer 83

ok save it and send it over so I can look at it

Answer 84

thanks, one sec

Answer 85

hmm somehow you have +8 and not -8 in cell A3...how odd

other than that, everything else looks perfect (ignoring row 3)

Answer 86

anyways, notice how when you look at row 7, the values in each column A, B and C are

-4, -3, -3

ie cell A7 = -4, cell B7 = -3 and cell C7 = -3

Answer 87

this tells us that

when x = -4, y = -3 (for equation 1)

AND

when x = -4, y = -3 (for equation 2)

Answer 88

Overall it equals out to be -4,-3?

Answer 89

so this proves that (-4,-3) is the solution because it satisfies both equations and make the tables have the same y output for the same given x input

Answer 90

Thanks you soo much!

Answer 91

sure thing

sure it's a long process, but once you get the hang of it, you can easily create tables of any size you want very quickly