Question

Help

Answer 1

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

Answer 2

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?

Answer 3

no not really

Answer 4

Just started the unit

Answer 5

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.

Answer 6

ok i still don't fully understand

Answer 7

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

Answer 8

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 \[\bf ~~4x - y = -11
\\-(4x + 6y = 10)\]

Answer 9

ok

Answer 10

So what would we get from there?

Answer 11

1?

Answer 12

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

Answer 13

x-y=1?

Answer 14

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

Answer 15

x

Answer 16

or does the x cancel out

Answer 17

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

Answer 18

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

Answer 19

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

Answer 20

-7y?

Answer 21

Correct. And -11-10 would be?

Answer 22

-1?

Answer 23

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

Answer 24

ok

Answer 25

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

Answer 26

3

Answer 27

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

Answer 28

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

Answer 29

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

am i right?

Answer 30

Let's please finish solving the example

Answer 31

ok

Answer 32

4x - 3y =-11

Answer 33

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

Answer 34

ok

Answer 35

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

Answer 36

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

Answer 37

Idk how to solve for the x in this part

Answer 38

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

Answer 39

x = 3

Answer 40

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

Answer 41

4

Answer 42

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

Answer 43

-2

Answer 44

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

Answer 45

ok

Answer 46

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

Answer 47

indeed and the only one that has that Is B

Answer 48

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

Answer 49

wym?

Answer 50

?

Answer 51

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

Answer 52

Oh i looked at b but saw the numbers different

Answer 53

Then would It Be C

Answer 54

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

Answer 55

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

Answer 56

I dont know really

Answer 57

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

Answer 58

No it wont work

Answer 59

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

Answer 60

really

Answer 61

8-27=-19 yes

Answer 62

oh ok

Answer 63

all I had to do was do 8-27

Answer 64

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

Answer 65

Yes

Answer 66

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

Answer 67

ok

Answer 68

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

Answer 69

i believe that D wouldn't work

Answer 70

What reason supports that belief?

Answer 71

Its really an educated guess

Answer 72

What is the "educated" in that educated guess?

Answer 73

a guess

Answer 74

So it's just a guess then

Answer 75

yes

Answer 76

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

Answer 77

ok

Answer 78

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

Answer 79

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

Answer 80

Well D is right too but yes, A is correct

Answer 81

Ok thanks alot

Answer 82

have a good night

Answer 83

U too, nite