Question

The sum of two numbers is -5. The difference is
13. What is the smaller number?

Answer 1

The smaller number is -9.

Explanation:

Let x and y be the two unknown numbers.

Their sum is -5. Hence:

`x+y=-5`

Their difference is 13. Hence:

`x-y=13`

This yields a system of equations. We can solve this using elimination. Adding the two equations together:

`(x+y)+(x-y)=(-5)+(13)`

Simplify:

`2x=8`

Divide both sides by two. Thus:

`x=4`

Using either equation (I'll use the first):

`(4)+y=-5\Rightarrow y=-9`

So, our two numbers are 4 and -9.

The smaller number is -9.