How to solve this substitution problem? (Algebra)?

the easiest way to solve this is substitution.
take the second equation, and solve for either m or n
m-n=8

m=8+n

Now... substitute what you got for m into the first equation

2(8+n)+n=1

16+2n+n=1

16+3n=1

3n=1-16

3n=-15

n=-5

equation1: 2m + n = 1
equation2: m - n = 8
we can rewrite equation 2 as
                m = 8 + n
we can substitute this equation 1.
2(8+n) + n = 1
16 + 2n + n = 1
16+ 3n = 1
3n = -15
n = -5

since m = 8 + n,
m = 8 + (-5)
m = 3

so m =3 and n = -5

2m + (n ........... )=1
.........(n = m - 8)
2m + .......m - 8 = 1 - - - and carry on.

after you find m, plug it into an equation to find n
then plug m and n into the other equation, and if answers match, you are done
otherwise, go back and retrace your steps and arithmetic computations.

You can either solve for a variable, lets say n, in the first equation and plug it into the second equation to get an answer or, much more easily, you can add the functions together to get rid of a variable

2m+n=1
+
m-n=8
________
3m = 9
m=3

since m = 3 n must equal -5 once m is plugged back into either of the initial given equations



If you don't see why I can add these functions together just think about this as an example:

2m + n = 1
+
3=3
_________

We know m-n = 8 much like 3=3 so when we add the same thing to both sides we are not doing any incorrect math.