Question

Find two numbers, if Their sum is − 1/3 and their difference is 18

Answer 1

Answer:

The two numbers are: -9.17 and 8.83

Step-by-step explanation:

Let the two numbers represent 'x' and 'y'

Their sum is − 1/3 ==>          x + y = -1/3  .................(eqn 1)

Their difference is 18 ==>    x − y = 18  ....................(eqn 2)

from equation 2,

x = 18 + y

therefore, substitute for 'x' in (eqn 1) to get y

(18+y) + y = -1/3

18 + 2y = -1/3

2y = -1/3 − 18

2y = -$18\frac{1}{3}$

2y = - 55/3

y = (-55/3) / 2

y = -55/3 x 1/2

y = -55/6 = -9.17

Substitute for 'y' in either equation

picking (eqn 2)

x − (-9.17) = 18

x + 9.17 = 18

x = 18 − 9.17

x = 8.83

Answer 2

Let the two numbers be $x,y$.

We have

$\begin{cases}x+y=-\frac{1}{3}\\x-y=18\end{cases}$

From the second equation, we derive $x=18+y$

Plugging this value in the first equation, we have

$18+y+y=-\dfrac{1}{3} \iff 2y=-\dfrac{1}{3}-18\iff 2y=-\dfrac{55}{3} \iff y=-\dfrac{55}{6}$

And we derive

$x=18+y=18-\dfrac{55}{6}=\dfrac{53}{6}$