PLEASE HELP
Two equations are given below:
m + 4n = 8
m = n − 2
What is the solution to the set of equations in the form (m, n)?
(4, 6)
(2, 4)
(0, 2)
(6, 8)

- anonymous

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- Vocaloid

first, let's leave the second equation alone for now and just look at
m+4n = 8
what do you get when you subtract 4n from each side?

- anonymous

M-N=4

- Vocaloid

hm, not quite, let's just try the left side first
what happens when you subtract 4n from m+4n?

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## More answers

- anonymous

M

- Vocaloid

right! now let's look at the right side
what happens when you subtract 4n from 8?

- anonymous

8N?

- Vocaloid

nope, since 8 has no variable and 4n has a variable, it's just
8 - 4n
understand so far?

- anonymous

Yes

- Vocaloid

ok, so the left side of the equation is m, and the right side of the equation is 8 - 4n,
which gives us
m = 8 - 4n
with me so far?

- anonymous

yes

- Vocaloid

good, so our first equation is
m = 8 - 4n
and our second equation is
m = n - 2
we have m by itself on the left side in both equations, so we can set the two equations equal to each other
8 - 4n = n - 2
can you try solving for n now?

- anonymous

I thing so would it be 4,6

- Vocaloid

not quite, let's just take this one step at a time
8 - 4n = n - 2
what happens when you add 2 to each side?

- anonymous

what do you mean

- Vocaloid

add 2 to the left side, add 2 to the right side, and tell me what is on each side

- anonymous

10-6n=2n-4

- Vocaloid

not quite, remember we want to leave 4n and n alone because these are variables

- anonymous

oh

- Vocaloid

left side is 8 - 4n, what do you get when you add 2?

- anonymous

10-4n

- Vocaloid

great! the right side is n - 2, what do you get when you add 2?

- anonymous

n-4

- Vocaloid

not quite, what is n-2+2?

- anonymous

2

- Vocaloid

not quite, think of it this way
n-2+2 means start with n, take away 2, then add 2 back
what is n-2+2?

- anonymous

2n

- Vocaloid

not quite, remember that we leave n alone since its a variable
one more time
n-2+2=?

- anonymous

oh

- anonymous

so basicly we just substract 2 from to then add it back correct

- Vocaloid

right, so what do we get in the end?

- anonymous

2-2=0+2=2 right?

- Vocaloid

uh, not quite...
let me try to explain it differently
I start with n marbles. I pick up 2 marbles, then I drop 2 marbles. How many marbles do I have?

- anonymous

0

- Vocaloid

hint: I started with n marbles

- anonymous

n

- Vocaloid

right!
so what does n-2+2=?

- anonymous

n

- Vocaloid

good!
so, on the left side we have 10-4n and on the right side we have n
10-4n = n
now, let's leave 10 alone since it's not a variable
what happens when we add 4n to each side?

- anonymous

we get 8n

- Vocaloid

not quite...
the left side is 10-4n, what do we get when we add 4n?

- anonymous

10-4n=4n

- Vocaloid

not quite, please try again
10-4n+4n=?

- anonymous

10-4n=6n+4n=10n?

- Vocaloid

not quite, remember that we leave the 10 alone since it's not a variable (doesn't have n)
10-4n+4n = ?

- anonymous

oh so 10-4n+4n=10-8n

- Vocaloid

not quite...
think of it this way:
I start with 10, take away 4n, then add 4n. what's left?

- anonymous

10-4n

- Vocaloid

not quite, let's try one more time
I start with 10 marbles, then I drop 4n marbles, then I pick up 4n marbles, how many marbles do I have?

- anonymous

14n? I am not sure

- Vocaloid

let's try something different
10-4+4=?

- anonymous

14

- Vocaloid

hint: A-B+B = A

- Vocaloid

so, if A-B+B = A, then what is 10-4n+4n?

- anonymous

14n

- Vocaloid

|dw:1436906201632:dw|

- anonymous

10

- Vocaloid

great!
so, the left side is 10
now let's move to the right side
the right side is n, what do you get when you add 4n?

- anonymous

4n

- Vocaloid

not quite, remember that we started with n
n+4n=?

- anonymous

oh so we just add 4 to the N

- Vocaloid

not quite...
hint: n+4n = (1+4)n

- anonymous

oh so the thing is 5n

- Vocaloid

great!
left side is 10
right side is 5n
10 = 5n
can you try solving for n now?

- anonymous

I believe so

- anonymous

I think it would equal 0,2

- Vocaloid

10 = 5n
n = ?

- anonymous

2

- Vocaloid

great! n = 2
going back to the original problem,
m = n − 2
so what is m?

- anonymous

0

- Vocaloid

great!
m=0
n=2
so what is (m,n)?

- anonymous

0,2

- Vocaloid

great, we're done!

- anonymous

yes

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