To solve the equations, we need to isolate the variable x in both equations.

First equation: 1.1x - 2 1/2 = 3/5x

To simplify, convert 2 1/2 to an improper fraction: 2 1/2 = 5/2

Now, rewrite the equation: 1.1x - 5/2 = 3/5x.

Get rid of the decimal by multiplying all terms by 10 to clear the decimal:
10(1.1x) - 10(5/2) = 10(3/5x)
11x - 25 = 6x

Now, isolate x by moving 6x to the other side:
11x - 6x = 25
5x = 25
x = 25/5
x = 5

Second equation: 6.75x = 2 1/4x - 9

Convert 2 1/4 to an improper fraction: 2 1/4 = 9/4

Now, rewrite the equation: 6.75x = 9/4x - 9.

Get rid of the decimal by multiplying all terms by 100 to clear the decimal:
100(6.75x) = 100(9/4x) - 100(9)
675x = 225x - 900

Now, isolate x by moving 225x to the other side:
675x - 225x = 900
450x = 900
x = 900/450
x = 2

Therefore, the solution to the system of equations is x = 5 and x = 2.