An excellent candidate for elimination.
20n + 50m = 20
can be rewritten 60n + 150m = 60
can be rewritten 60n + 150m = 60
70m + 30n = 29
can be rewritten 140m + 60n = 58
can be rewritten 140m + 60n = 58
since both equations, in their new form, have 60n, just subtract the second equation from the first
60n + 150m - 140m - 60n = 60 - 58
10m = 2
m = 1/5
10m = 2
m = 1/5
substitute that value into the first equation
20n + 50(1/5) = 20
20n + 10 = 20
20n = 10
n = 1/2
20n + 50(1/5) = 20
20n + 10 = 20
20n = 10
n = 1/2
check by substituting those values into the second equation
70(1/5) + 30(1/2) = 29
14 + 15 = 29
70(1/5) + 30(1/2) = 29
14 + 15 = 29
Always check your work using an equation other than the one you used to calculate any of the variables (Because you could be solving a system of more than two equations.)
