if 2m + n= 7, then 9m+3n=

Question

i tried using elimination for this one too. I tried to find m
m= 7-n/2

Then i plugged it into the first equation. and somehow i got 7=7

??? CAN SOMEONE PLEASE EXPLAIN

Answer 1

from 2m + n= 7
n = 7 - 2m

now plug that into 9m+3n
= 9n + 3(7-2m)
= 9n +21 - 6m
= 3m + 21

your way should have said:
m = (7 - n)/2
then 9m + 3n
= 9(7-n)/2 + 3n
= (63 - 9n)/2 + 6n/2
= (63 - 3n)/2

checking:
if we let n = 5, then from yours m = 1
and 9m + 3n = (63 - 15)/2 = 24 ---> from your solution
9m + 3n = 3(1) + 21 = 24 ---> from mine
9m + 3n = 9(1) + 3(5) = 24 ----> from our choices of n and m

Answer 2

I get what you are saying.. but 24 isn't one of the answer choices.

A) 7/9
B) 7/3
C) 10
D) 21
E) 63

Answer 3

for two unknowns (m and n) you need two unique equations for a solution

since there is only one complete equation
... the 2nd equation must be similar

it seems that the 9 may be a typo
... probably a 6 instead

6m + 3n = 3 (2m + n) = 21

Answer 4

I didn't say that 24 was the only answer, there is no unique answer.
It is the answer only if we let m = 1 and n = 5

Since, as Scott pointed out, you did not state a second equation
9m + 3n can only be expressed in terms of either m or n