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



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x, y - the numbers

The sum of the two numbers is 9.
[tex]x+y=9[/tex]

If one number is subtracted from the other, the result is 3.
[tex]x-y=3[/tex]

Solve the system of equations:
[tex]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[/tex]

The numbers are 6 and 3.
Let's say x to the first number and y to the second one.
We add them : [tex]x+y=9[/tex]
Then we substract them : [tex]x-y=3[/tex]
Now we add the equations: 

[tex](x+y)+(x-y)=9+3\\ x+x+y-y=12\\ 2x=12\\ \\ x=\frac { 12 }{ 2 } \\ \\ x=6[/tex]

and finally rewrite the equation:

[tex]6+y=9\\ y=9-6\\ y=3\\ \\ x=6\quad and\quad y=3[/tex]

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