Find a fraction which reduce to 2/3 if the numerator and the denominator are each increased by 1 and reduce to 3/5 if the numerator and the denominator are each reduced by 2

Answer 1

original fraction --- x/y

first new fraction: (x+1)/(y+1) = 2/3
3x + 3 = 2y + 2
3x - 2y = -1 **

second new fraction: (x-2)/(y-2) = 3/5
5x - 10 = 3y - 6
5x - 3y = 4 ***

solve the two equations ** and ***