Solve the system graphically and algebrically

- anonymous

Solve the system graphically and algebrically

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- anonymous

x+y=1
y=2/3x-4

- anonymous

@freckles

- anonymous

You're looking for x and y?

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- anonymous

I dont know:(

- anonymous

Okay, well I believe you are because it says solve. There are two options here. Do you want the easy way or the harder way? (They aren't always easy versus hard, it just happens that one is a lot simpler in this instance)

- anonymous

easy way:)

- anonymous

Okay for the easy way in this instance, we will go with substitution. Do you know what that is?

- anonymous

yes.

- anonymous

Okay so use substitution by plugging in what the second equation gives you for "y" into the first equation. It should look like this: \[x+2/3x-4=1\]
You can solve this because it is one variable.

- anonymous

So solve for x

- anonymous

1^2/3x=5 ??

- anonymous

I'm not sure where you got one from.
Step one: add 4 to both sides. You get: \[x+2/3x=5\]

- anonymous

Step two: combine like terms. You get:\[5/3x=5\]

- anonymous

Do you get it so far?

- anonymous

yes:)

- anonymous

Step three: multiply each side by three (to get rid of the denominator): \[5x=15\]

- anonymous

Now what do you do?

- anonymous

x=3

- anonymous

Correct. Now, plug in what you just found for "x" into the first equation. Your equation should look like this now: \[3+y=1\]

- anonymous

ok:) Now what do we do?

- anonymous

Solve for "y" can you do that part by yourself?

- anonymous

i suppose. Is it y=-3x-1?

- anonymous

Nope. You plugged in an "x" for no reason. From your equation 3+y=1, all you have to do is subtract 3 from each side. You end up with: \[y=-2\]

- anonymous

Alright:)

- anonymous

Get that?

- phi

btw the question asks
Solve the system graphically and algebarically
it wants you to solve this problem both ways.

- anonymous

Okay so now we know that you have x=3 and y=-2. I don't have any way to graph it myself, but I plugged this into wolfram alpha so look at this graph:
http://www.wolframalpha.com/input/?i=x%2By%3D1%2C+y%3D%282%2F3%29x-4

- anonymous

Thank you! So, we solved it graphically, what would be the 'algebracially' part?

- anonymous

Well, since we found x=3 and y=-2, we can (if you want) turn it into a coordinate. I'm not sure if that's what your question wants, but based on the fact you need to graph it also, then turn it into a coordinate. It'll be (3,-2)

- anonymous

I'm guessing that your problem also wants you to graph the two equations.

- anonymous

But that would be your answer.

- anonymous

tHANKS<3 Can I ask another??

- anonymous

Sure but I'm not sure if I'll be able to answer everything.

- anonymous

it's fine.

- anonymous

|dw:1439058745006:dw|
Solve and graph

- anonymous

Let me see what I can do, give me a second. I might be able to help, but maybe not.

- anonymous

ok,if not, we can always call @phi lol

- anonymous

Yeah I'm sorry I kinda remember how to do this, but I'm not sure enough to help you. I don't want you to get it wrong.

- anonymous

it's cool :) Thanks anywayss

- anonymous

No problem. Good luck!

- phi

\[|x-1| -3 \le 1 \]
first add (write) +3 on both sides

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