Solve the system of equations using elimination by addition?

6m - n = 41 …… [1]
m - 6n = -34 …… [2]

[1] × (-6) :
-36m + 6n = -246 …… [3]

[2] + [3] :
-35m = -280
m = (-280)/(-35)
m = 8

Substitute m = 8 into [1] :
6 × 8 - n = 41
48 - n = 41
n = 7

Hence, m = 8 and n = 7

You want to multiply 6m-n=41 by -6 to get an additive inverse in both equations.
-36m+6n=-246
m-6n=-34
Add the equations together so the n cancels out
-35m=280
Solve
m=-8
Plug m in
8-6n=-34
Solve.
n=7