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

First, let's solve for y in the first equation:

2x + 11y = 15
11y = 15 - 2x
y = (15 - 2x)/11

Now, we can substitute this expression for y into the second equation:

10x - 11((15 - 2x)/11) = 9
10x - 15 + 2x = 9
12x - 15 = 9
12x = 24
x = 2

Now that we have found the value of x, we can substitute it back into the first equation to find the value of y:

2(2) + 11y = 15
4 + 11y = 15
11y = 11
y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.