5m - n = 31 (eq. 1)
m - 5n = -13 (eq. 2)
Multiplying equation 2 by 5 at both sides of the equal sign, we get:
5(m - 5n) = 5*(-13)
5m - 5*5n = -65
5m - 25n = -65 (eq. 3)
Subtracting equation 3 to equation 1, we get:
5m - n = 31
-
5m - 25n = -65
-------------------------
24n = 96
n = 96/24
n = 4
Substituting this result into equation 1 and solving for m:
5m - 4 = 31
5m = 31 + 4
m = 35/5
m = 7