Question

The sum of two numbers is 15 and their difference is 7, What are the two numbers

Answer 1

These numbers are 11 and 4

11+4=15
11-4=7

Answer 2

Greetings!

Let x represent the first number
Let y represent the second number

Create a system of equations, representing the problem:

`\left \{ {{x+y=15} \atop {x-y=7}} \right.`

Use elimination to solve:

`+ \frac{\left \{ {{x+y=15} \atop {x-y=7}} \right. }{2x=22}`

Divide both sides by 2.

`2x=22`

`(2x)/(2)= (22)/(2)`

`x=11`

Solve for the other variable:

`x+y=15`

`11+y=15`
Add -11 to both sides.

`(11+y)+(-11)=(15)+(-11)`

`y=4`

The Solution to this Problem is:

`\left[\begin{array}{ccc}x=11,y=4\end{array}\right]`

The numbers are 11 and 4.

Hope this helps.
-Benjamin