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

We have the equations:

We can multiply the first equation by 5 to match the coefficients of x in both equations:

5(x + 2y) = 5(11)
5x + 10y = 55

Now, we have the equations:

Subtract the second equation from the first equation to eliminate x:

(5x + 10y) - (5x - 3y) = 55 - 3
5x + 10y - 5x + 3y = 52
13y = 52
y = 4

Now, substitute y = 4 into the first equation to solve for x:

x + 2(4) = 11
x + 8 = 11
x = 3

Therefore, the solution to the system of equations is x = 3 and y = 4.