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

Let's use the substitution method.

From the first equation, we can solve for x in terms of y:
x = (17 + 6y) / 6

Now, we can substitute this expression for x into the second equation:
5((17 + 6y) / 6) - y = 23
(85 + 30y) / 6 - y = 23
85 + 30y - 6y = 138
24y = 53
y = 53 / 24
y = 2.2083

Now, we can substitute this value of y back into the first equation to solve for x:
x = (17 + 6(2.2083)) / 6
x = (17 + 13.25) / 6
x = 30.25 / 6
x = 5.0417

Therefore, the solution to the system of equations is x = 5.0417 and y = 2.2083.