Solve by substitution method?

Question

6m + n = 31

m - 3n = 21

Answer 1

m = 21 + 3n
6(21 + 3n) + n = 31
126 + 18n + n = 31
19n = - 95
n = - 5

m + 15 = 21
m = 6

m = 6 , n = - 5

Answer 2

Substitution...

6m + n = 31
m - 3n = 21

The second equation, so that m stands alone
m = 3n + 21

Plug the m = into the first equation...
6(3n + 21) + n = 31
18n + 126 + n = 31
19n = -95
n = -5

Then the second equation...
m - 3n = 21
m - 3(-5) = 21
m + 15 = 21 (2 negatives make a positive)
m = 6

So...
m = 6
n = -5

But that's a little weird...since you said the first equation was 6m + n =31
It doesn't work.

6m + n = 31
6(6) + 5 = 31
36 + 5 = 31
41 = 31???
And the people who answered after me have the same answer, so I should be right.

Are you sure you don't mean 6m - n = 31?
Because
6m - n = 31
6(6) - 5 = 31
36 - 5 = 31
31 = 31

Answer 3

6m + n = 31
m - 3n = 21 => m = 3n + 21

Sub the second equation into the first:
6(3n + 21) + n = 31
18n + 126 + n = 31
19n = 31 - 126
19n = -95
n = -5

Sub n=-5 into m = 3n + 21:
m = 3(-5) + 21
m = -15 + 21
m = 6

Answer 4

I think I already answered one of the substitution questions you put up. Follow the directions I gave you then and you should come up with the answer.

Answer 5

6m+n=31
n=31-6m.....(1)

m-3n=21
m-3(31-6m)=21(from (1)
m-93+18m=21
m+18m=21+93
19m=114
m=114/19

m=6...(2)

n=31-6m
n=31-6(6)...frm(2)
n=31-36
n= -5

m=6
n= -5

Answer 6

6m+n=31, n=31-6m........................(1)
m-3n=21......................................(2)
substitute (1)into (2).
m-93+18m=21
19m=114
m=6,n=31-36=-5
Answer=(6,-5).