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

Answer:

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

Step-by-step 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 = $-\frac{2}{5}$

Plug the value of "y" into either equations.

x + $(-\frac{2}{5})$ = 0

Add $\frac{2}{5}$ to both sides.

x = $\frac{2}{5}$