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

From the first equation:
x + 2y = 550
x = 550 - 2y

Now substitute x into the second equation:

5(550 - 2y) + 3y = 1700
2750 - 10y + 3y = 1700
-7y = -1050
y = 150

Now substitute y back into one of the original equations to solve for x:

x + 2(150) = 550
x + 300 = 550
x = 550 - 300
x = 250

Therefore, the solution to the system of equations is x = 250 and y = 150.