Question

the sum of two numbers is 9. if one number is subtracted from the other, the result is 3. find the numbers

Answer 1

Let's say x to the first number and y to the second one.
We add them : $x+y=9$
Then we substract them : $x-y=3$
Now we add the equations: 

$(x+y)+(x-y)=9+3\\ x+x+y-y=12\\ 2x=12\\ \\ x=\frac { 12 }{ 2 } \\ \\ x=6$

and finally rewrite the equation:

$6+y=9\\ y=9-6\\ y=3\\ \\ x=6\quad and\quad y=3$

Answer 2

X, y - the numbers

The sum of the two numbers is 9.
$x+y=9$

If one number is subtracted from the other, the result is 3.
$x-y=3$

Solve the system of equations:
$x+y=9 \\ \underline{x-y=3} \\ x+x=9+3 \\ 2x=12 \ \ \ |\div 2 \\ x=6 \\ \\ x+y=9 \\ 6+y=9 \ \ \ |-6 \\ y=3$

The numbers are 6 and 3.