To determine if two numbers can both have a difference of 8 and a sum of 1, we can set up a system of equations. Let’s denote the two numbers as x and y.
According to the given conditions, we can write the following equations:
- Equation 1 (sum):
x + y = 1 - Equation 2 (difference):
x - y = 8
Now, we can solve this system step by step:
- From Equation 1, we can express y in terms of x:
y = 1 - x - Next, we substitute this expression for y into Equation 2:
x - (1 - x) = 8- This simplifies to:
x - 1 + x = 8 - Combining like terms gives:
2x - 1 = 8 - Now, add 1 to both sides:
2x = 8 + 12x = 9 - Finally, divide by 2:
x = 4.5
Now that we have the value of x, let’s find y:
y = 1 - 4.5 = -3.5
So, the two numbers are 4.5 and -3.5.
Let’s verify:
- Difference:
4.5 - (-3.5) = 4.5 + 3.5 = 8(correct) - Sum:
4.5 + (-3.5) = 1(correct)
Thus, yes, it is indeed possible for two numbers to have a difference of 8 and a sum of 1, as evidenced by the numbers 4.5 and -3.5.