Final answer:
By substituting the expression from the first equation into the second equation, we find that q = -5. Then, substituting q back into the first equation, we find p = -3. Thus, the solution to the system is p = -3 and q = -5.
Step-by-step explanation:
To find the solution to the system of equations by substitution, we start with the given equations p = q + 2 and 3p + 2q = -19. We can substitute the expression for p from the first equation into the second equation, which gives us 3(q + 2) + 2q = -19. Simplifying this, we get 3q + 6 + 2q = -19, and combining like terms we have 5q + 6 = -19. Solving for q, we subtract 6 from both sides to obtain 5q = -25, and then divide by 5 to get q = -5. We can then substitute q back into the first equation and solve for p: p = (-5) + 2, which gives us p = -3. Hence, the solution to the system is p = -3 and q = -5.