Question

Decide whether you would use the graphing, substitution, or elimination method to solve the following system of equations. Explain, in complete sentences, why you chose that method.
Part 2: Solve the following system of equations and show all of your work.

4x + 3y = -1
3x + y = 3

Answer 1

Um,

Eq(2)=)

3x + y = 3

y=3-3x---(3)

Now put y or Eq(3) in Eq(1)

4x + 3y = -1

Answer 2

Hang on, @mikala1
Maybe you ought to do the 'deciding' part first?

Answer 3

She is gonna do substitution only because she never gets the elimination @terenzreignz

Answer 4

Well, whatever works, I guess :)

Answer 5

can some one show me how to do this one in elimination

Answer 6

@mikala1 See what i have showed.

Answer 7

yes i do thank you

Answer 8

That was substitution, though.

Answer 9

could you show the elimination to me plz

Answer 10

First, let's do a quick review of the properties of equality, just so you know what you're doing...
First let's assume
a = b
c = d

and n is some real number.

Answer 11

First, we could multiply n to both sides of the equation, and the equality holds:
a = b
na = nb

Answer 12

Also, we could add the left-hand sides of the equation, and this would be equal to the sum of the right-hand sides of the equation:
a = b
c = d

a + c = b + d

Answer 13

You understand these?

Answer 14

yes so far

Answer 15

Okay, we are going to apply them...
Back to the system of equations...

4x + 3y = -1
3x + y = 3

The trick here is to make use of that second property I showed you, where you "add" both equations. Getting it so far?

Answer 16

yes

Answer 17

We *could* go ahead and add both equations outright :
(4x + 3y) + (3x + y) = -1 + 3
7x + 4y = 2

But this doesn't really help us, right?

Answer 18

no not really

Answer 19

This is where the first property comes in :)
We want to make it so that adding the equations gets rid of one of the unknowns.
Let's rewrite that system:
4x + 3y = -1
3x + y = 3

We want to get rid of one of these unknowns (either x or y)
In time, you'll learn to recognise which is easier to eliminate, but for now, take my word for it that y is easier to eliminate. Getting it so far?

Answer 20

yes thank you keep going i will say if i dont understand

Answer 21

I'd prefer you solve this yourself, though. I'll guide you through it.
Again, rewriting the system:
4x + 3y = -1
3x + y = 2

We want to get rid of y, right?
Look at the first equation. What do you add to 3y so that you get zero?

Answer 22

you will add -1 right?

Answer 23

No. My question was
What was it you add to 3y so that you get 0...
In symbols
3y + ? = 0
Is it clearer now?

Answer 24

im not sure what you add i thought the teacher siad -1 or 4 x

Answer 25

well, you could just sort of find the value of that "?" there
3y + ? = 0
and you bring 3y to the other side to get
? = -3y

Understand it now? :)

Answer 26

yes so its 3

Answer 27

not just 3
you add -3y
or in other words
you subtract 3y

Get it?

Answer 28

yes i for got the y sorry about that

Answer 29

Back to the system:
4x + 3y = -1
3x + y = 2

You know that in the first equation, you need to somehow add "-3y" to get rid of the y, right?

Answer 30

yes and i only needed the fisrt one helped on

Answer 31

So, that's your hint. You have to somehow acquire a "-3y" at your second equation. How do you go about that? (HINT: Use the first property of equality we discussed)

Answer 32

ok thank you so much

Answer 33

You already get it? Brilliant :)

Answer 34

yes i did thank you