Take x + y = 7, and solve for x to get: x = 7 - y
Take (x + 1)(y – 1) = 6, and substitute the x-value from the above equation to get: (7 - y + 1)(y – 1) = 6
Simplify: (8 - y)(y – 1) = 6
Use FOIL to expand: 8y - 8 - y² + y = 6
Multiply both sides of the equation by -1 to get: -8y + 8 + y² - y = -6
Simplify and set equal to zero: y² - 9y + 14 = 0
Factor: (y - 2)(y - 7) = 0
This means either y = 2 or y = 7.

case i: If y = 2, we can substitute this value into the first equation to get x + 2 = 7, which means x = 5. In this case, xy = (5)(2) = 10
case ii: If y = 7, we can substitute this value into the first equation to get x + 7 = 7, which means x = 0. In this case, xy = (0)(7) = 0


Answer: C.F