1. Problem statement: Given the sequence $-8, x, y, 19$ in an arithmetic progression, find $x$ and $y$. 2. In an arithmetic progression, consecutive terms differ by a common difference $d$. 3. With four terms the common difference is $d = \frac{a_4 - a_1}{3}$. 4. Substitute $a_1 = -8$ and $a_4 = 19$ to get $d = \frac{19 - (-8)}{3} = \frac{27}{3} = 9$. 5. Now compute $x = a_2 = a_1 + d = -8 + 9 = 1$. 6. Next compute $y = a_3 = a_2 + d = 1 + 9 = 10$. 7. Final answer: $x = 1$ and $y = 10$.