Substitute 2m + n =0 and m + 2n =3

There are several ways you can solve this problem if you're trying to solve for m and n. You can substitute, or systems of equations. However, I'm going to use substitution:

2m + n = 0 => n = -2m

We can input that in for the other equation:

m + 2n = 3 now becomes: m + 2(-2m) = 3

Now we can solve:

m + 2(−2m) = 3

m + −4m = 3

(m + −4m) = 3 (Combine Like Terms)

−3m=3

m = -1

Now we can input that value in to solve for n:

We said that n = -2m, and m = -1, so n = -2(-1):

n = 2

Your final answer is m = -1, and n = 2, which can also be written as (m,n) = (-1,2)

However, if you were solving for m+n:

You would add the two equations!:

2m + n = 0

m + 2n = 3

3m + 3n = 3

Now, you can take 3 common:

3(m+n) = 3

m + n = 1

Your final answer for what m + n equals 1!