BioHazard9064
  • BioHazard9064
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Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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BioHazard9064
  • 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
  • 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
  • BioHazard9064
no not really

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BioHazard9064
  • BioHazard9064
Just started the unit
anonymous
  • 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
  • BioHazard9064
ok i still don't fully understand
BioHazard9064
  • 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
  • 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
  • BioHazard9064
ok
anonymous
  • anonymous
So what would we get from there?
BioHazard9064
  • BioHazard9064
1?
anonymous
  • anonymous
Seperate the three different values. So \[\bf 4x-4x=?\\~and~\\-y-6y=?\\~and~\\-11-10=?\]
BioHazard9064
  • BioHazard9064
x-y=1?
anonymous
  • anonymous
Can you solve those three things I have there? What is 4x-4x?
BioHazard9064
  • BioHazard9064
x
BioHazard9064
  • BioHazard9064
or does the x cancel out
anonymous
  • anonymous
No, it would be 0. The x's cancel out.
BioHazard9064
  • BioHazard9064
and y-y6 would be y or would it cancel out aswell
anonymous
  • anonymous
-y-6y is the same as -1-6.
BioHazard9064
  • BioHazard9064
-7y?
anonymous
  • anonymous
Correct. And -11-10 would be?
BioHazard9064
  • BioHazard9064
-1?
anonymous
  • anonymous
That would be if it was -11+10. -11-10=-21
BioHazard9064
  • BioHazard9064
ok
anonymous
  • anonymous
So what we have left is \[\bf -7y=-21\] Now solve for y
BioHazard9064
  • BioHazard9064
3
anonymous
  • anonymous
Correct. So now substitute \[\bf y=3\] into the top section of the problem and solve for x
anonymous
  • anonymous
The "top section" would be \[\bf 4x - y = -11\] by the way
BioHazard9064
  • BioHazard9064
given what you showed me me so far it would be B. 4x + 3y = 5 2y = -6 am i right?
anonymous
  • anonymous
Let's please finish solving the example
BioHazard9064
  • BioHazard9064
ok
BioHazard9064
  • BioHazard9064
4x - 3y =-11
anonymous
  • anonymous
\[\bf 4x-3=-11\]
BioHazard9064
  • BioHazard9064
ok
BioHazard9064
  • BioHazard9064
So then we would solve the bottom part 2x + 3y = 5
anonymous
  • anonymous
What? Solve for x in \[\bf 4x-3=-11\]
BioHazard9064
  • BioHazard9064
Idk how to solve for the x in this part
anonymous
  • anonymous
\[\bf 3x=9\] Can you solve for x here?
BioHazard9064
  • BioHazard9064
x = 3
anonymous
  • anonymous
How about this one? \[\bf 3x-3=9\]
BioHazard9064
  • BioHazard9064
4
anonymous
  • anonymous
How about this one \[\bf 4x-3=-11\] Solve it the same way as that last one.
BioHazard9064
  • BioHazard9064
-2
anonymous
  • anonymous
Correct. So now we have solved the example \[\bf x=-2\\y=3\]
BioHazard9064
  • BioHazard9064
ok
anonymous
  • anonymous
I suppose you could just plug those values into the options and see which ones work.
BioHazard9064
  • BioHazard9064
indeed and the only one that has that Is B
anonymous
  • anonymous
Are you sure? B doesn't check out with me.
BioHazard9064
  • BioHazard9064
wym?
anonymous
  • anonymous
?
anonymous
  • anonymous
\[\bf 2(3) \neq -6\]
BioHazard9064
  • BioHazard9064
Oh i looked at b but saw the numbers different
BioHazard9064
  • BioHazard9064
Then would It Be C
anonymous
  • anonymous
\[\bf 9(-2)=-6?\]
BioHazard9064
  • BioHazard9064
sorry im really tired so sorry if im not 100% in to it
BioHazard9064
  • BioHazard9064
I dont know really
anonymous
  • anonymous
Let's go over A \[\bf x=-2\\y=3\\~\\-4x - 9y = -19\] Plug em in and see if they work
BioHazard9064
  • BioHazard9064
No it wont work
anonymous
  • anonymous
i don't know how to say this, but it does work.
BioHazard9064
  • BioHazard9064
really
anonymous
  • anonymous
8-27=-19 yes
BioHazard9064
  • BioHazard9064
oh ok
BioHazard9064
  • BioHazard9064
all I had to do was do 8-27
anonymous
  • anonymous
\[\bf x=-2\\y=3\\~\\-10y=-30\] Does it work?
BioHazard9064
  • BioHazard9064
Yes
anonymous
  • anonymous
So then A is all good. Now let's check D.
BioHazard9064
  • BioHazard9064
ok
anonymous
  • anonymous
\[\bf x=-2\\y=3\\~\\12x - 3y = -33\]
BioHazard9064
  • BioHazard9064
i believe that D wouldn't work
anonymous
  • anonymous
What reason supports that belief?
BioHazard9064
  • BioHazard9064
Its really an educated guess
anonymous
  • anonymous
What is the "educated" in that educated guess?
BioHazard9064
  • BioHazard9064
a guess
anonymous
  • anonymous
So it's just a guess then
BioHazard9064
  • BioHazard9064
yes
anonymous
  • anonymous
Here's a pro-tip for turning your guesses into certainty: \[\huge Do\\\huge the\\\huge work\]
BioHazard9064
  • BioHazard9064
ok
anonymous
  • anonymous
\[\bf x=-2\\y=3\\~\\12x - 3y = -33\]
BioHazard9064
  • BioHazard9064
ok sorry im told I got to get off but I think its A am i right?
anonymous
  • anonymous
Well D is right too but yes, A is correct
BioHazard9064
  • BioHazard9064
Ok thanks alot
BioHazard9064
  • BioHazard9064
have a good night
anonymous
  • anonymous
U too, nite

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