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- BioHazard9064

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- BioHazard9064

Choose the equivalent system of linear equations that will produce the same solution as the one given below.
4x - y = -11
2x + 3y = 5
A. -4x - 9y = -19
-10y = -30
B. 4x + 3y = 5
2y = -6
C.7x - 3y = -11
9x = -6
D.12x - 3y = -33
14x = -28

- anonymous

So then solve the first one and write down the results you get from it. Then solve the other ones until you get the same answers. Do you know how to solve systems of linear equations at all?

- BioHazard9064

no not really

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## More answers

- BioHazard9064

Just started the unit

- anonymous

Here is a website to get started with them: http://www.purplemath.com/modules/systlin1.htm After you read a little and get a better understanding of them, I'll help you go through this problem.

- BioHazard9064

ok i still don't fully understand

- BioHazard9064

is the answer B? because thats what I got before I just want to be sure cuz i have not done this in forever

- anonymous

Well then let's go over the example in your question together. \[\bf 4x - y = -11
\\2x + 3y = 5\] In my opinion, the substitution method is my favorite so let's use that one first. When we use substitution, we want to get rid of either the x or y value. We do this by making those values equal to each other. In this example, I would probably choose to get rid of the x value by multiplying the bottom half by 2. \[\bf 4x - y = -11
\\2(2x + 3y = 5)\]\[\bf 4x - y = -11
\\4x + 6y = 10\] Now we are going to subtract the bottom line from the top \[\bf ~~4x - y = -11
\\-(4x + 6y = 10)\]

- BioHazard9064

ok

- anonymous

So what would we get from there?

- BioHazard9064

1?

- anonymous

Seperate the three different values. So \[\bf 4x-4x=?\\~and~\\-y-6y=?\\~and~\\-11-10=?\]

- BioHazard9064

x-y=1?

- anonymous

Can you solve those three things I have there? What is 4x-4x?

- BioHazard9064

x

- BioHazard9064

or does the x cancel out

- anonymous

No, it would be 0. The x's cancel out.

- BioHazard9064

and y-y6 would be y or would it cancel out aswell

- anonymous

-y-6y is the same as -1-6.

- BioHazard9064

-7y?

- anonymous

Correct. And -11-10 would be?

- BioHazard9064

-1?

- anonymous

That would be if it was -11+10. -11-10=-21

- BioHazard9064

ok

- anonymous

So what we have left is \[\bf -7y=-21\] Now solve for y

- BioHazard9064

3

- anonymous

Correct. So now substitute \[\bf y=3\] into the top section of the problem and solve for x

- anonymous

The "top section" would be \[\bf 4x - y = -11\] by the way

- BioHazard9064

given what you showed me me so far it would be
B. 4x + 3y = 5
2y = -6
am i right?

- anonymous

Let's please finish solving the example

- BioHazard9064

ok

- BioHazard9064

4x - 3y =-11

- anonymous

\[\bf 4x-3=-11\]

- BioHazard9064

ok

- BioHazard9064

So then we would solve the bottom part 2x + 3y = 5

- anonymous

What? Solve for x in \[\bf 4x-3=-11\]

- BioHazard9064

Idk how to solve for the x in this part

- anonymous

\[\bf 3x=9\] Can you solve for x here?

- BioHazard9064

x = 3

- anonymous

How about this one? \[\bf 3x-3=9\]

- BioHazard9064

4

- anonymous

How about this one \[\bf 4x-3=-11\] Solve it the same way as that last one.

- BioHazard9064

-2

- anonymous

Correct. So now we have solved the example \[\bf x=-2\\y=3\]

- BioHazard9064

ok

- anonymous

I suppose you could just plug those values into the options and see which ones work.

- BioHazard9064

indeed and the only one that has that Is B

- anonymous

Are you sure? B doesn't check out with me.

- BioHazard9064

wym?

- anonymous

?

- anonymous

\[\bf 2(3) \neq -6\]

- BioHazard9064

Oh i looked at b but saw the numbers different

- BioHazard9064

Then would It Be C

- anonymous

\[\bf 9(-2)=-6?\]

- BioHazard9064

sorry im really tired so sorry if im not 100% in to it

- BioHazard9064

I dont know really

- anonymous

Let's go over A \[\bf x=-2\\y=3\\~\\-4x - 9y = -19\] Plug em in and see if they work

- BioHazard9064

No it wont work

- anonymous

i don't know how to say this, but it does work.

- BioHazard9064

really

- anonymous

8-27=-19 yes

- BioHazard9064

oh ok

- BioHazard9064

all I had to do was do 8-27

- anonymous

\[\bf x=-2\\y=3\\~\\-10y=-30\] Does it work?

- BioHazard9064

Yes

- anonymous

So then A is all good. Now let's check D.

- BioHazard9064

ok

- anonymous

\[\bf x=-2\\y=3\\~\\12x - 3y = -33\]

- BioHazard9064

i believe that D wouldn't work

- anonymous

What reason supports that belief?

- BioHazard9064

Its really an educated guess

- anonymous

What is the "educated" in that educated guess?

- BioHazard9064

a guess

- anonymous

So it's just a guess then

- BioHazard9064

yes

- anonymous

Here's a pro-tip for turning your guesses into certainty: \[\huge Do\\\huge the\\\huge work\]

- BioHazard9064

ok

- anonymous

\[\bf x=-2\\y=3\\~\\12x - 3y = -33\]

- BioHazard9064

ok sorry im told I got to get off but I think its A am i right?

- anonymous

Well D is right too but yes, A is correct

- BioHazard9064

Ok thanks alot

- BioHazard9064

have a good night

- anonymous

U too, nite

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