Question 100024
Let x=the numerator
And let y=the denominator

Now we are told that:

2x=y+2-----------------------eq1
and
(x+3)/(y+3)=2/3-------------------eq2

multiply each term in eq2 by 3(y+3) to get rid of fractions and we get:

3(x+3)=2(y+3)  get rid of parens
3x+9=2y+6  subtract 9 from both sides:

3x=2y-3---------------------eq2
multiply eq1 by 2 and subtract it from eq2:
eq2-2*(eq1)=

 3x=2y-3
-4x=-2y-4

-x=-7 or

x=7-----------------numerator
substitute x=7 into eq1

2*7=y+2  subtract 2 from both sides

14-2=y

y=12-----------denominator

CK

(7+3)/(12+3)=2/3

10/15=2/3
2/3=2/3

also
2*7=12+2
14=14


Hope this helps-----ptaylor