The sum of two numbers is nine if one number is subtracted from the other the result is - 1 find the numbers

Lets make x and y the two numbers. The sum of the two numbers (x and y) is 9 means that they add to 9. So the first equation is

x+y = 9

Let's isolate y by subtracting x from both sides. That gives us

y = 9-x

The other bit of information given is "if one number is subtracted from the other, the result is - 1", which means we have this other equation

x-y = - 1

From here, substitute y for 9-x

x-y = - 1

x - (y) = - 1

x - (9-x) = - 1

x-9+x=-1

2x-9 = - 1

2x-9+9 = - 1+9

2x = 8

2x/2 = 8/2

x = 4

If x = 4, then y is ...

y = 9-x

y = 9-4

y = 5

Therefore, the two numbers are 4 and 5. They add to 9

4+5 = 9

and they subtract to - 1

4-5 = - 1

Final Answer: 4 and 5