Algebra 1 Word problem

Question

The larger of two numbers is twice the smaller number increased by 21. The difference of the two numbers is negative 13. Find the two numbers.

Answer 1

Let L=larger number; S=smaller number

L=2S+21 (larger number is twice the smaller number increased by 21)

S-L=-13 (smaller number minus the larger number because the difference is negative)

Substitute the L from the first equation into the second equation to get:

S-(2S+21)=-13

S-2S-21=-13 (distributive property)

Simplify to get S=-8

Then substitute S=-8 into the first equation to get L=5

So, the numbers are -8 and 5