Solve the system graphically and algebrically

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Solve the system graphically and algebrically

Mathematics
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x+y=1 y=2/3x-4
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I dont know:(
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)
easy way:)
Okay for the easy way in this instance, we will go with substitution. Do you know what that is?
yes.
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.
So solve for x
1^2/3x=5 ??
I'm not sure where you got one from. Step one: add 4 to both sides. You get: \[x+2/3x=5\]
Step two: combine like terms. You get:\[5/3x=5\]
Do you get it so far?
yes:)
Step three: multiply each side by three (to get rid of the denominator): \[5x=15\]
Now what do you do?
x=3
Correct. Now, plug in what you just found for "x" into the first equation. Your equation should look like this now: \[3+y=1\]
ok:) Now what do we do?
Solve for "y" can you do that part by yourself?
i suppose. Is it y=-3x-1?
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: \[y=-2\]
Alright:)
Get that?
  • phi
btw the question asks Solve the system graphically and algebarically it wants you to solve this problem both ways.
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
Thank you! So, we solved it graphically, what would be the 'algebracially' part?
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)
I'm guessing that your problem also wants you to graph the two equations.
But that would be your answer.
tHANKS<3 Can I ask another??
Sure but I'm not sure if I'll be able to answer everything.
it's fine.
|dw:1439058745006:dw| Solve and graph
Let me see what I can do, give me a second. I might be able to help, but maybe not.
ok,if not, we can always call @phi lol
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.
it's cool :) Thanks anywayss
No problem. Good luck!
  • phi
\[|x-1| -3 \le 1 \] first add (write) +3 on both sides

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