Answer: The two numbers are 9 and 5
9+5 = 14
9-5 = 4
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Step-by-step explanation:
Let x and y be the unknown numbers. I'll make x the larger item.
The original instructions translate to these equations
x+y = 14
x-y = 4
Add the equations straight down
- The x terms add to 2x
- The y terms add to 0 and go away
- The right hand sides add to 14+4 = 18
We have the new equation 2x = 18 which solves to x = 9
If x = 9, then y = 5 because we can see that either
x+y = 14
9+y = 14
y = 14-9
y = 5
or,
x-y = 4
9-y = 4
-y = 4-9
-y = -5
y = 5
Therefore, the two numbers are 9 and 5.
A quick check verifies this:
9+5 = 14
9-5 = 4