Question 141359
This would be the system of equations I would come up with:

b=s+8    read as b is s plus 8
b+3=2(s+3)    read as 3 more than b is 2 times 3 more than s

Solve by substituting the solution for b in the first equation into the second.
That is done as follows:

s+8+3=2s+6
5=s

This means that Barry's sister is 5 years old.

Now, to find Barry's age we plug in s=5 into the first equation:

b=5+8=13. Barry is 13.

Let's check this:

Is Barry currently 8 years older than his sister who is 5? Yes, 5+8=13.
In 3 years, will Barry be twice as old as his sister? 5+3=8; 13+3=16; 2(8)=16; Yes.