The sum of two numbers is 41 and the difference is 17 . What are the numbers?

Let the two numbers be x and y.

"The sum of two numbers is 41" becomes x + y = 41.

"the difference is 17" becomes x - y = 17.

Write one equation under the other:

x + y = 41

x - y = 17

Add down the three columns to get 2x + 0 y = 58.

So 2x = 58 means x = 29.

29 + y = 41 means y = 12

OK...we have

x + y =41    and

x - y = 17   adding the two equations, we have

2x = 58   divide by two on both sides

x = 29

And, using the first equation to find y, we have

29 +  y = 41     subtract 29 from both sides

y = 12

And that's it......x = 29 and y = 12   !!!!