A first number plus twice a second number is 24. twice the first number plus the second totals 21. find the numbers.

We do like the following:

Set the first number is a and the second is b.

We have two equations: a+2xb=24, 2xa+b=21

And we have 2xa+4xb=48 or 2xa=48-4xb

So: 48-4xb+b=21 or - 3xb=21-48=-27 and we got b=-27: (-3) = 9 and a = 6

a=6 and b=9