Question

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)

Answer 1

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?

Answer 2

M-N=4

Answer 3

hm, not quite, let's just try the left side first

what happens when you subtract 4n from m+4n?

Answer 4

M

Answer 5

right! now let's look at the right side

what happens when you subtract 4n from 8?

Answer 6

8N?

Answer 7

nope, since 8 has no variable and 4n has a variable, it's just

8 - 4n
understand so far?

Answer 8

Yes

Answer 9

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?

Answer 10

yes

Answer 11

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?

Answer 12

I thing so would it be 4,6

Answer 13

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?

Answer 14

what do you mean

Answer 15

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

Answer 16

10-6n=2n-4

Answer 17

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

Answer 18

oh

Answer 19

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

Answer 20

10-4n

Answer 21

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

Answer 22

n-4

Answer 23

not quite, what is n-2+2?

Answer 24

2

Answer 25

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?

Answer 26

2n

Answer 27

not quite, remember that we leave n alone since its a variable

one more time

n-2+2=?

Answer 28

oh

Answer 29

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

Answer 30

right, so what do we get in the end?

Answer 31

2-2=0+2=2 right?

Answer 32

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?

Answer 33

0

Answer 34

hint: I started with n marbles

Answer 35

n

Answer 36

right!

so what does n-2+2=?

Answer 37

n

Answer 38

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?

Answer 39

we get 8n

Answer 40

not quite...

the left side is 10-4n, what do we get when we add 4n?

Answer 41

10-4n=4n

Answer 42

not quite, please try again

10-4n+4n=?

Answer 43

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

Answer 44

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

10-4n+4n = ?

Answer 45

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

Answer 46

not quite...

think of it this way:

I start with 10, take away 4n, then add 4n. what's left?

Answer 47

10-4n

Answer 48

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?

Answer 49

14n? I am not sure

Answer 50

let's try something different

10-4+4=?

Answer 51

14

Answer 52

hint: A-B+B = A

Answer 53

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

Answer 54

14n

Answer 55

10

Answer 56

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?

Answer 57

4n

Answer 58

not quite, remember that we started with n

n+4n=?

Answer 59

oh so we just add 4 to the N

Answer 60

not quite...

hint: n+4n = (1+4)n

Answer 61

oh so the thing is 5n

Answer 62

great!

left side is 10
right side is 5n

10 = 5n

can you try solving for n now?

Answer 63

I believe so

Answer 64

I think it would equal 0,2

Answer 65

10 = 5n
n = ?

Answer 66

2

Answer 67

great! n = 2

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

Answer 68

0

Answer 69

great!

m=0
n=2

so what is (m,n)?

Answer 70

0,2

Answer 71

great, we're done!

Answer 72

yes