Is it possible for two numbers to have a difference of 8, and a sum of 1?

Solution:

We have to find two possible numbers which have a difference of 8 and a sum of 1.

Let x be the first number and y be the second number.

Given, x - y = 8 ---------- (1)

x + y = 1 --------------- (2)

Adding (1) and (2)

x - y + x + y = 8 + 1

2x = 9

x = 9/2 or 4.5

Substitute the value of x in (1)

9/2 - y = 8

y = 9/2 - 8

y = (9 - 16) / 2

y = -7/2 or -3.5

Verification:

The difference of two numbers is 8

x - y = 8

LHS = 4.5 - (-3.5)

= 4.5 + 3.5

= 8

RHS = 8

LHS = RHS

The sum of two number is 1

x + y = 1

LHS = 4.5 + (-3.5)

= 4.5 - 3.5

= 1

RHS = 1

LHS = RHS

Hence proved.

Therefore, the two possible numbers are x = 4.5 and y = -3.5.

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Is it possible for two numbers to have a difference of 8, and a sum of 1?

Summary:

The two possible numbers to have a difference of 8 and sum of 1 are x = 4.5 and y = -3.5.