The difference between two numbers is one. Three times the larger number minus two times the smaller number is 9. What is the value of the larger number?

What we need to do is set up a system of equations:
a - b = 1 (the difference b/n the two is 1)
3a - 2b = 9 (3 times the larger minus 2 times the smaller equals 9)

From here, you can solve this through elimination by multiplying the first equation by -2, or by substitution by isolating the a-variable.