Final answer:
The two numbers are -16 and 5.
Step-by-step explanation:
To solve this problem, we can create two equations based on the given information.
Let's say one number is x and the other number is y.
The sum of the two numbers is -11, so we can write the equation x + y = -11. We also know that one number is 21 more than the other, so we can write the equation x = y + 21.
Now we can solve these equations simultaneously to find the values of x and y.
Substituting the value of x in the second equation, we have y + 21 + y = -11.
Combining like terms, we get 2y + 21 = -11.
Subtracting 21 from both sides, we have 2y = -32.
Dividing both sides by 2, we get y = -16.
Plugging this value back into the equation x = y + 21, we find x = -16 + 21, which gives us x = 5.
Therefore, the two numbers are -16 and 5. Option A (-6, 15) is incorrect, Option B (-10, 31) is incorrect, Option C (-8, 29) is incorrect, and Option D (-13, 32) is incorrect.