your two numbers are x and y
x/y=6
x+y=21
solve one of the two equations for one of the two variables and then substitute the solution into the other equation
solve the first equation for x
multiply both sides by y
x=6y
sutstitute 6y in for x in the second equation
6y+y=21
7y=21
divide both sides by 7
y=3
Now substitute 3 in for y
3+x=21
subtract 3 from each side
x=18
larger number is 18
smaller number is 3