1. **State the problem:** We need to find the value of $b - a$ for an integer point $(a,b)$ with $a > 9$ that satisfies the system of inequalities: $$x + y < 50$$ $$y - x > 28$$ 2. **Rewrite inequalities:** From the first inequality: $$y < 50 - x$$ From the second inequality: $$y > x + 28$$ 3. **Combine inequalities:** The point $(a,b)$ must satisfy: $$x + 28 < y < 50 - x$$ 4. **Find integer values for $a$ and $b$:** Since $a > 9$ and both $a,b$ are integers, $b$ must be an integer strictly between $a + 28$ and $50 - a$. 5. **Check feasibility:** For such $b$ to exist, the interval $(a + 28, 50 - a)$ must contain at least one integer. This requires: $$a + 28 < 50 - a$$ $$2a < 22$$ $$a < 11$$ Since $a > 9$ and $a < 11$, possible integer values for $a$ are $10$ only. 6. **Find $b$ for $a=10$:** $$10 + 28 < b < 50 - 10$$ $$38 < b < 40$$ The only integer $b$ satisfying this is $b = 39$. 7. **Calculate $b - a$:** $$b - a = 39 - 10 = 29$$ **Final answer:** $$\boxed{29}$$