Question

Algebra 2 help please? I give medals.
Let y be the difference of two numbers such that one number varies directly as x while the other number varies inversely as x. If y = –7 when x = –2, and y = 5 when x = 1, express y in terms of x.

Answer 1

Let the numbers be a&b
Then y=a-b,Let a>b
also a=kx,where k is a constant.
and\[b=\frac{ l }{ x }\]
where l is a constant.
when x=-2,a=-2k,\[b=\frac{ l }{ -2 },y=-7\]
\[-7=-2k+\frac{ l }{ 2 },~or~-14=-4k+l ...(1)\]
when x=1,a=k,b=l/1=l,y=5 ...(2)
adding (1) & (2)
-9=-3k
k=3
5=3-l
l=-2
a=3x
\[b=\frac{ -2 }{ x }\]
\[Hence~y=3x+\frac{ 2 }{ x }\]