Question

18. MP Reason Inductively The product of

two integers is -24. The difference
between the two integers is 14. The sum of
the two integers is 10. What are the two
integers?

Answer 1

- 2 and 12

Explanation:

let the 2 integers be x and y , x > y , then

x - y = 14 → (1)

x + y = 10 → (2)

add the 2 equations term by term to eliminate y

2x = 24 ( divide both sides by 2 )

x = 12

Substitute x = 12 into (2)

12 + y = 10 ( subtract 12 from both sides )

y = - 2

As a check

x + y = 12 + (- 2) = 12 - 2 = 10

x - y = 12 - (- 2) = 12 + 2 = 14

xy = 12 × - 2 = - 24