Simultaneous equations using subsitution?

Question

Please, I'm so confused...
If you have
3m-n=11
3m-2n=15
Using substitution, how would you solve this? When you isolate the variable, does it become : -n= 11-3m?

Answer 1

Here are two different ways to solve these equations.

First way:
3m - n = 11, so 3m = 11 + n. (I added n to both sides.)
3m - 2n = 15, so 3m = 15 + 2n. (I added 2n to both sides.)
Then 11 + n = 15 + 2n since both sides are equal to 3m.
Now subtract n + 15 from both sides.
So 11 - 15 = 2n - n = n, or n = -4.
From above, 3m = 11 + n = 11 + (-4) = 11 - 4 = 7.
Then m = 7/3. The solution is m = 7/3 and n = -4.

Second way:
You are right when you say -n = 11 - 3m (you got this using the first equation) ,
but notice that this is the same as n = 3m - 11 (multiply both sides by -1). Now n is isolated, so you substitute it into the second equation and get 3m - 2n = 3m -2(3m - 11) =
3m - 6m + 22 = 15. Then 22 - 15 = 6m - 3m = 3m, so
3m = 7, or m = 7/3.
Go back to n = 3m - 11 and put in the value m = 7/3.
n = (3)(7/3) - 11 = 7 - 11 = -4.
The solution is m = 7/3 and n = -4 , the same as it was before!

To check, notice that 3m - n = (3)(7/3) - (-4) = 7 + 4 = 11
and 3m - 2n = (3)(7/3) -(2)(-4) = 7 - (-8) = 7 + 8 = 15.

Answer 2

if 3m-n=11, then 3m=11+n so then m=(11+n)/3

3((11+n)/3) -2n = 15
3(11/3 + n/3) -2n = 15
11+n-2n=15
-n=4
n=-4

3m-(-4)=11
3m=11-4
3m=7
m=7/3 = 2 1/3

Answer 3

3m-n=11
-n=11-3m
n=3m-11

3m-2(3m-11)=15
3m-6m+22=15
-3m=-7
m=7/3

So m=7/3 and when you use that in either equation, n= -4.
Hope this helps!