Question

The sum of two numbers is zero. When 13 times the smaller number is added to 8 times the larger, the result is 2. Find the two numbers.

Answer 1

x = (2/5); y = (-2/5)

Explanation:

x + y = 0

13x + 8y = 2

Multiply so the "x" variables are opposite with the same absolute value.

(-13) x + y = 0 (-13) ⇒ -13x - 13y = 0

(1) 13x + 8y = 2 (1) ⇒ 13x + 8y = 2

Add the two equations.

(13x - 13x) + (8y - 13y) = (2 - 0)

-5y = 2

Divide both sides by -5

y =
`-(2)/(5)`

Plug the value of "y" into either equations.

x +
`(-(2)/(5))` = 0

Add
`(2)/(5)` to both sides.

x =
`(2)/(5)`