Answer: The value of p and q for which the system of equations represent coincident lines is p = 2 and q = 1.
Step-by-step explanation: To represent coincident lines, the two lines must be proportional. Therefore, the slope of the second line must be equal to the slope of the first line.
The slope of the first line is 3/2. The slope of the second line is p + 2q + 2/p + q + 1. Therefore, we set these two equal:
3/2 = p + 2q + 2/p + q + 1.
Cross multiplying, we get:
3(p + q + 1) = 2(p + 2q + 2).
Simplifying, we get:
3p + 3q + 3 = 2p + 4q + 4.
Combining like terms, we get:
p - q = 1.
Therefore, the value of p and q for which the system of equations represents coincident lines is p = 2 and q = 1.