Question

The sum of two integers with different signs is 8. Give two possible integers that fit this description

Answer 1

9 and -1
10 and -2
11 and -3
12 and -4
13 and -5
14 and -6
15 and -7
.
.
.
etc.

There are an infinite number of possible pairs that fit this description.

Answer 2

Anything that fits the equation x-y=8 would answer this problem.

If x=1, then y=-7; if x=2, then y=-6.

You would choose a number for x and plug it into the equation.  Then you would subtract this value from both sides and divide both sides by -1 to get your answer.  

For example, if x=1:
1-y=8
1-y-1=8-1
-y=7
-y/-1=7/-1
y=-7

There are an infinite number of solutions for this.