To solve this system of equations, we can use the method of substitution or elimination.

Let's use the substitution method:

From the first equation:
3x + y = 9
y = 9 - 3x

Substitute y = 9 - 3x into the second equation:
2x - (9 - 3x) = 1
2x - 9 + 3x = 1
5x - 9 = 1
5x = 10
x = 2

Now, substitute x = 2 back into the first equation to find y:
3(2) + y = 9
6 + y = 9
y = 3

Therefore, the solution to the system of equations is x = 2 and y = 3.