Use and augmented matrix to solve the system.
x + y = 5
3x - y = -1
From what I can I read, it seems it would be (3,5) but that is not one of the answer choices.
I would rather have an explanation than an answer. I think the matrix is:
[1 1]5]
[3 -1]-1]
Any help is greatly appreciated.

Question

Use and augmented matrix to solve the system.
x + y = 5
3x - y = -1
From what I can I read, it seems it would be (3,5) but that is not one of the answer choices.
I would rather have an explanation than an answer. I think the matrix is:
[1 1]5]
[3 -1]-1]
Any help is greatly appreciated.

fibonaccichick666 · Answer

That would be the matrix of coefficients

fibonaccichick666 · Answer

and it is correct

fibonaccichick666 · Answer

What you want to do is reduce the matrix using Reduced Row Echelon(I think thats the term or its Gauss but you get it)  you want it of the form: $$\left[\begin{matrix}1 & 0 & x \ 0 & 1 & y\end{matrix}\right]$$

anonymous · Answer

I found what to do in the back of the book, could you stick around and see if I get the right answer?

fibonaccichick666 · Answer

sure

fibonaccichick666 · Answer

Any progress?

anonymous · Answer

Well, apparently x=y+2.333.... I think I am lost lol

fibonaccichick666 · Answer

yea, it's alright lets try from the beginning

fibonaccichick666 · Answer

So you have :$$\left[\begin{matrix}1 & 1 & 5 \ 3 & -1 & -1\end{matrix}\right]$$ right?

anonymous · Answer

Yes. Now you multiply the second row by -2 and add it to the first right?

fibonaccichick666 · Answer

to type the matrix, right click on mine and hit show math as tex commands it'll make your life easier.  Why -2?

fibonaccichick666 · Answer

and why second?

anonymous · Answer

That is what my book says...

fibonaccichick666 · Answer

I disagree.  Does your book have the answer too? ( I would like to check myself)

anonymous · Answer

It is not for this equation, it was the only thing I could find on matrices.

fibonaccichick666 · Answer

oh ok not quite then.  I was like I know I checked my answer at least 3 times... lol alright so in order to solve a matrix you want to get a 1 in the top left first.  do we have that?

anonymous · Answer

Yes.

fibonaccichick666 · Answer

now you want all zeroes directly below it, how do we achieve this? we have two weapons.  
1. we can multiply the first row by something.
2. We can add the first row to any other row.

So can you think of a way to get a zero where the three is?

anonymous · Answer

You can add -3 to get zero.

fibonaccichick666 · Answer

right so what does that give you? remember you have to add the whole row

anonymous · Answer

That row would be [0 -4|-4]

fibonaccichick666 · Answer

-4?

anonymous · Answer

-1+(-3)?

fibonaccichick666 · Answer

remember the entire row, the columns stay together so the second column would be -4 but what about the third?

anonymous · Answer

Oh, doesn't that stay the same?

fibonaccichick666 · Answer

nope same rule, as the others

anonymous · Answer

The 3rd would be -4 then?

fibonaccichick666 · Answer

no, first what i 3*5?

anonymous · Answer

15

fibonaccichick666 · Answer

k now what is -15+-1

anonymous · Answer

-16. Where did the 5 come from?

fibonaccichick666 · Answer

The last column from the original matrix  do you see it?

anonymous · Answer

That is the first row, arn't we working on the second though lol

fibonaccichick666 · Answer

nope, remember if we are adding rows, we add the whole row so -3[ 1 1 5] + [3 -1 -1]

anonymous · Answer

Ohhhh, I get it now lol.

fibonaccichick666 · Answer

good! yay! ;P

fibonaccichick666 · Answer

so can you tell me what the second row becomes?

anonymous · Answer

[0 -4|-16]

fibonaccichick666 · Answer

correct now can you make the first non-zero in the second row =1?

anonymous · Answer

Add 5 to it

fibonaccichick666 · Answer

no remember you can only multiply the row or add another row to it

anonymous · Answer

Multiply the row by -0.25. Then you have have [0 1|4]

fibonaccichick666 · Answer

that is correct! now you want any number above that 1 to be 0  can you do it?

anonymous · Answer

By just doing what we did for the second row right?

fibonaccichick666 · Answer

mmhmm

anonymous · Answer

Could you just subtract the 2nd row from the first?

fibonaccichick666 · Answer

yea, but you want to think of it as adding minus 1 time the second

anonymous · Answer

Yea, end up with the same answer though :P. So in the end it would be 
[1 0 | -19]
[0 1 | 4]

fibonaccichick666 · Answer

-19???

anonymous · Answer

Guess I mixed that one up too. Adding -4?

fibonaccichick666 · Answer

yea but adding it to what?

anonymous · Answer

the -15...?

fibonaccichick666 · Answer

ahh ok, sorry I just had no clue how you got the rest and then that so the -15 was only when we multiplied the first row by -3 that doesn't actually stay,  the first row remains  [1 1 5] until we add another row to it or reduce it using multiplication

anonymous · Answer

Oh. So it is only [ 1 0 | 1]? The answer would be (1,4) I assume.

fibonaccichick666 · Answer

yup yup

anonymous · Answer

Thanks a bunch :). I might message you if I have a problem with another question like this. Have a nice day :)

fibonaccichick666 · Answer

so this is what we are doing: http://www.purplemath.com/modules/systlin6.htm

fibonaccichick666 · Answer

in case you need reference.  good luck and your welcome!