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

Let's use the substitution method.

From the second equation, we can solve for x in terms of y:
x = 1 + 2y

Now we substitute this expression for x into the first equation:
3(1 + 2y) + y = 17
3 + 6y + y = 17
7y + 3 = 17
7y = 14
y = 2

Now that we have found the value of y, we can substitute it back into the second equation to find the value of x:
x - 2(2) = 1
x - 4 = 1
x = 5

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