let the first number be x and the second number be y

so you have the equation:

x+y = 9 since their sum is 9

you also have the equation:

3y - 2x = 7 from the second sentence.  solve for x in the first equation and substitute it in for x in this equation

x = 9-y

3y - 2(9-y) = 7

3y - 18 + 2y = 7

5y - 18 = 7

5y = 25

y = 25

plug this back in the equation for x

x = 9-y

x = 9-5

x = 4

so the numbers are 4 and 5