Answer:
The numbers are [tex]-\frac{2}{3}[/tex] and [tex]18\frac{2}{3}[/tex]
Step-by-step explanation:
Let x and y be the numbers
According to the statement, "The sum of two number is 18.", first equation will be:
[tex]x+y = 18\ \ \ \ Eqn\ 1[/tex]
And according to "The sum of two number is 18. 5 times the first number subtracted from 4/7bof the second number is 14." Second equation will be:
[tex]\frac{4}{7}y-5x = 14[/tex]
Multiplying whole equation by 7
[tex]7*\frac{4}{7}y-7*5x = 7*14\\4y-35x=98\\-35x+4y = 98\ \ \ \ Eqn\ 2[/tex]
From equation 1
[tex]x+y = 18\\y = 18-x[/tex]
Putting this in second equation
[tex]-35x+4(18-x) = 98\\-35x+72-4x= 98\\-39x = 98-72\\-39x = 26\\\frac{-39x}{-39} = \frac{26}{-39}\\x = -\frac{2}{3}[/tex]
Putting x = -2/3 in equation 1
[tex]-\frac{2}{3}+y = 18\\y = 18+\frac{2}{3}\\y = 18\frac{2}{3}[/tex]
Hence, the numbers are [tex]-\frac{2}{3}[/tex] and [tex]18\frac{2}{3}[/tex]
