Question

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

Answer 1

Answer:

The smaller number is -9.

Step-by-step 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.