To find two numbers that meet the criteria of having a sum of 11 and a difference of 9, we can set up two equations based on the information given.
Let the two numbers be x and y.
From the problem, we know:
- x + y = 11 (1)
- x – y = 9 (2)
Now, we can solve these equations step by step. First, we can solve equation (2) for x:
x = y + 9
Next, we can substitute this expression for x into equation (1):
(y + 9) + y = 11
Combining like terms gives:
2y + 9 = 11
Now, subtract 9 from both sides:
2y = 2
Dividing both sides by 2:
y = 1
Now that we have y, we can substitute back to find x:
x = 1 + 9 = 10
So the two numbers are 10 and 1.
To verify, we can check:
- Sum: 10 + 1 = 11
- Difference: 10 – 1 = 9
Both conditions are satisfied, confirming that the numbers are indeed 10 and 1.