Question

The sum of two numbers is 17 and their difference is 7?

Answer 1

`5,12`

Explanation:

We can represent the first number with `a` and the second number as `b`. What do we know?

Their sum has to be `color(blue)17`
Their difference has to be `color(red)7`
Given this, we can set up a system of equations:

`a+b=color(blue)17`
`a-b=color(red)7`

If we add our two systems, the `b` terms will cancel, and we're left with:

`2a=24`

`=>color(purple)(a=12)`

Our first number is `a`. Now, we plug `12` in for `a` into both equations. We get:

`12+b=17`

`=>b=5`

`12-b=7`

`=>color(purple)(b=5)`

`a` is `12`, and `b` is `5`. These are our two numbers.