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,
[tex]x=y-9\ldots\ldots\ldots\text{.}(1)[/tex]
2) Five times the first is 14 more than 6 times the second number.
The equation is,
[tex]5x=6y+14\ldots\ldots\ldots\text{.}(2)[/tex]
Solve the equations for x and y,
[tex]\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}[/tex]
Put the value of y in equation 1,
[tex]\begin{gathered} x=y-9 \\ x=-59-9 \\ x=-68 \end{gathered}[/tex]
Hence, the two numbers are x= -68 and y= -59.
