if 2m + n= 7, then 9m+3n=
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
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
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
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
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
To solve this problem, we'll start with the given equation:
2m + n = 7 ---(Equation 1)
Your approach of using elimination is correct. Let's start by eliminating the variable 'n' from the two equations.
To do that, we'll multiply Equation 1 by 3 and Equation 2 by 1 (to make the coefficients of 'n' the same but with opposite signs):
3(2m + n) = 3(7) ---(Equation 1 multiplied by 3)
9m + 3n = 21 ---(Equation 3)
Next, we'll multiply Equation 1 by 1 and Equation 2 by 2 (to make the coefficients of 'n' the same but with opposite signs):
2(2m + n) = 2(7) ---(Equation 1 multiplied by 2)
4m + 2n = 14 ---(Equation 4)
Now, we have:
9m + 3n = 21 ---(Equation 3)
4m + 2n = 14 ---(Equation 4)
To eliminate the variable 'n', we'll subtract Equation 4 from Equation 3:
(9m + 3n) - (4m + 2n) = 21 - 14
Simplifying, we get:
5m + n = 7 ---(Equation 5)
Now we have two equations:
2m + n = 7 ---(Equation 1)
5m + n = 7 ---(Equation 5)
Since the equations are now simpler, we can easily solve them using elimination or substitution.
If we subtract Equation 1 from Equation 5:
(5m + n) - (2m + n) = 7 - 7
Simplifying, we get:
3m = 0
This indicates that m = 0.
Now that we have the value of 'm', we can substitute it back into either Equation 1 or Equation 5. Let's substitute it into Equation 1:
2(0) + n = 7
n = 7
So the values of 'm' and 'n' are 0 and 7, respectively.
Finally, let's substitute these values into the second equation you provided:
9m + 3n = 9(0) + 3(7)
9m + 3n = 0 + 21
9m + 3n = 21
Therefore, 9m + 3n equals 21, which verifies the final result.