If twice the numerator is 2 more than the denominator and if 3 is added to each, new fraction is 2/3

In a rational number,
twice the numerator is 2 more than the denominator.
If 3 is added to each i.e. the numerator and the denominator, the new fraction is 2/3.

Find the original number?

Solution -

let the numerator be a and the denominator b. One of the equations is 2a=b+2. The other equation is (a+3)/b+3)=2/3. The solution gives a=7 and b=12. First check 2*7=12+2. Second check (7+3)/(12+3)=2/3