Question

I need help finding both the first and second number.

Answer 1

Let, x be the first number nad y be the second number.

1)One number is the nine less than the second number.

It can be written in the form of equation as,

`x=y-9\ldots\ldots\ldots\text{.}(1)`

2) Five times the first is 14 more than 6 times the second number.

The equation is,

`5x=6y+14\ldots\ldots\ldots\text{.}(2)`

Solve the equations for x and y,

`\begin{gathered} x-y=-9 \\ 5x-6y=14 \\ \text{Multiply equation 1 by 5 and take subtraction,} \\ 5(x-y)-(5x-6y)=5(-9)-14 \\ 5x-5y-5x+6y=-59 \\ y=-59 \end{gathered}`

Put the value of y in equation 1,

`\begin{gathered} x=y-9 \\ x=-59-9 \\ x=-68 \end{gathered}`

Hence, the two numbers are x= -68 and y= -59.