Question

Part 1: Explain, in complete sentences, how you would use the graphing method to solve the following system of equations. (3 points)

Part 2: Provide the solution to the system. (2 points)

Part 3: Explain what the solution represents on the graph. (1 point)

3x – 6y = 12
9x + 2y = –24

I have this so far but I don't know how to get the solution. 2- 3x-6y=12
-3x -3x
y= -3x+12
----------
-6
9x+2y= -24
-9x -9x
y= -9x-24
---------
2

Answer 1

Do you understand how to graph and get the answer?

Answer 2

No I suck at this :(

Answer 3

Don't say that. Ok so do you know how to graph the first equation?

Answer 4

I'm guessing I would graph it at 0,-3?

Answer 5

or (0,-6)

Answer 6

Let's start by solving for y. That will make this easier :) (I know you did it already but I'd like you to do it again) Please show all of your steps no matter how insignificant they may seem.

Answer 7

3x – 6y = 12
-3x -3x
-6y= -3x+12
---- ------
-6 -6
y= -3x +12
-------
-6
9x + 2y = –24
-9x -9x
2y= -9x - 24
--- -------
2 2
y= -9x - 24
-----
2

Answer 8

ok so I have a quick demo if you like http://www.educreations.com/lesson/view/jaylene/9305370/

Answer 9

But that looks good. an you distribute the -6 for the first eq. then simplify?

Answer 10

y= -3x - 6
---
-6
y= -9x -12
---
2

Answer 11

not quite. What is \(\frac{12}{6}=?\)

Answer 12

2

Answer 13

so its y = -3x - 2
----
-6

Answer 14

so the first eq. we have \[y=\frac{-3x+12}{-6}\] We distribute the -6 to get: \[y=\frac{-3x}{-6} +\frac{12}{-6}\]

Answer 15

Can you simplify this?

Answer 16

y =-3y - 2
-----
-6

Answer 17

simplify the x term please

Answer 18

y = 2x - 2

Answer 19

\(\frac{3}{6}=2?\)

Answer 20

0.5 but its a decimal?

Answer 21

yep, or one half either representation works

Answer 22

so when x=0 y=?

Answer 23

-2? idk

Answer 24

that's right good guess

Answer 25

just plug in x=0 then whatever you get is your answer.

Answer 26

that is how you find points to plot for a graph

Answer 27

but how do i get the solution of both equations?

Answer 28

You will do the same thing with the other eq. solve for y (also referenced as the standard form of a line) then graph. After you graph, you will notice that the lines intersect. On a graph, that is your answer. The coordinates of that point. It is where the lines are equal.

Answer 29

i got (4,1)

Answer 30

I do not agree. I got x=-5

Answer 31

so its (-5,1) ?

Answer 32

no

Answer 33

did you graph it?

Answer 34

yeah but since the second equation is y=- 9 x - 12 made it hard so i can't see it clearly
---
2

Answer 35

Yes the second eq is \(y=\frac{-9}{2}x -12\) maybe graphing isn't the best way to get a specific answer, just a nice ball park. Could you solve for x if I told you that the y terms are equal?

Answer 36

how do i do that?

Answer 37

So can you set the eq = to each other? We solved for y because we know that when these two lines intersect both their x and y coordinates are the same. If you set them =, you can find the x where the lines intersect.

Answer 38

I have to go in 5 but I'll write a sample problem for you and post it in a min.

Answer 39

http://www.educreations.com/lesson/view/jaylene2/9305862/ here you go a fully solved ex. problem

Answer 40

good luck!

Answer 41

Thank you for the help!