Let the two numbers be [tex]x,y[/tex].
We have
[tex]\begin{cases}x+y=-\frac{1}{3}\\x-y=18\end{cases}[/tex]
From the second equation, we derive [tex]x=18+y[/tex]
Plugging this value in the first equation, we have
[tex]18+y+y=-\dfrac{1}{3} \iff 2y=-\dfrac{1}{3}-18\iff 2y=-\dfrac{55}{3} \iff y=-\dfrac{55}{6}[/tex]
And we derive
[tex]x=18+y=18-\dfrac{55}{6}=\dfrac{53}{6}[/tex]
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 = -[tex]18\frac{1}{3}[/tex]
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
