Mathematics: Plx explain how to do this ty

Plx explain how to do this ty - id3883683, lexhorton2002

21gl13826

23.07.2022

The numbers are $-\frac{2}{3}$ and $18\frac{2}{3}$

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:

$x+y = 18\ \ \ \ Eqn\ 1$

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:

$\frac{4}{7}y-5x = 14$

Multiplying whole equation by 7

$7*\frac{4}{7}y-7*5x = 7*14\\4y-35x=98\\-35x+4y = 98\ \ \ \ Eqn\ 2$

From equation 1

$x+y = 18\\y = 18-x$

Putting this in second equation

$-35x+4(18-x) = 98\\-35x+72-4x= 98\\-39x = 98-72\\-39x = 26\\\frac{-39x}{-39} = \frac{26}{-39}\\x = -\frac{2}{3}$

Putting x = -2/3 in equation 1

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

Hence, the numbers are $-\frac{2}{3}$ and $18\frac{2}{3}$

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