Greetings!
Let x represent the first number
Let y represent the second number
Create a system of equations, representing the problem:
[tex] \left \{ {{x+y=15} \atop {x-y=7}} \right. [/tex]
Use elimination to solve:
[tex]+ \frac{\left \{ {{x+y=15} \atop {x-y=7}} \right. }{2x=22} [/tex]
Divide both sides by 2.
[tex]2x=22[/tex]
[tex] \frac{2x}{2}= \frac{22}{2} [/tex]
[tex]x=11[/tex]
Solve for the other variable:
[tex]x+y=15[/tex]
[tex]11+y=15[/tex]
Add -11 to both sides.
[tex](11+y)+(-11)=(15)+(-11)[/tex]
[tex]y=4[/tex]
The Solution to this Problem is:
[tex] \left[\begin{array}{ccc}x=11,y=4\end{array}\right] [/tex]
The numbers are 11 and 4.
Hope this helps.
-Benjamin
