Hard math question that i dont get :(

In class today, my teacher said that tomorrow on the test there is going to be a similar problem to this. could someone please walk me through the steps on solving it? Heres the question:

If 1 is added to the numerator of a fraction and 2 subtracted from the denominator, the result is equivalent to 2. If 1 is subtracted from the numerator of the same fraction and 2 added to the denominator, the result is equivalent to 1/3. What is the fraction?

X+1 / Y-2 =2

X-1/Y+2 = 1/3

SO:

X+1 = 2Y - 4

3X-3 = Y+2

-6X+6 = -2Y -4

-5X+7 = -8

X= 3

Y = 4

3/4