To solve this system of inequalities and equations, we can start by simplifying the inequality:

11/17 < a/b < 23/29

To compare fractions, we need to find a common denominator. The least common multiple of 17 and 29 is 493. So, we can rewrite the inequality as:

11(29)/493 < a/b < 23(17)/493
319/493 < a/b < 391/493

Now, we can rewrite the inequality in terms of a:

319/b < a < 391/b

Next, we can simplify the equation:

8b - 9a = 31

Rearranging the equation, we get:

9a = 8b - 31
a = (8b - 31)/9

Now, we can substitute the expression for a into the inequality:

319/b < (8b - 31)/9 < 391/b

Multiplying through by 9b to clear the denominator, we get:

319(9) < 8b - 31 < 391(9)
2871 < 8b - 31 < 3519

Adding 31 to all parts of the inequality, we get:

2902 < 8b < 3550

Dividing by 8, we get:

362.75 < b < 443.75

Therefore, the solution to the system of inequalities and equations is:

362.75 < b < 443.75
319/b < a < 391/b

where a = (8b - 31)/9.