Answer:
The smaller number is -9.
Step-by-step explanation:
Let x and y be the two unknown numbers.
Their sum is -5. Hence:
[tex]x+y=-5[/tex]
Their difference is 13. Hence:
[tex]x-y=13[/tex]
This yields a system of equations. We can solve this using elimination. Adding the two equations together:
[tex](x+y)+(x-y)=(-5)+(13)[/tex]
Simplify:
[tex]2x=8[/tex]
Divide both sides by two. Thus:
[tex]x=4[/tex]
Using either equation (I'll use the first):
[tex](4)+y=-5\Rightarrow y=-9[/tex]
So, our two numbers are 4 and -9.
The smaller number is -9.
