Question

For the following pairs of equations, how to write s in terms of a only? : 1) 3s-ah=a^2 and as+2h=3a 2) as=s+h and ah=a+h.

Answer 1

(1) `s=(5a^2)/(6+a^2)` and (2) `s=a/(a-1)^2`

Explanation:

As we have three variables `a,s` and`h`, we eliminate `h` to get `s` in terms of `a` only.

(1) As `3s-ah=a^2`, `ah=3s-a^2` and `h=3s/a-a`

and as `as+2h=3a`, `2h=3a-as` and `h=3/2a-(as)/2`

hence `3s/a-a=3/2a-(as)/2`

and multiplying each term by `2a`, we get

`6s-2a^2=3a^2-a^2s`

or `s(6+a^2)=5a^2` or `s=(5a^2)/(6+a^2)`

(2)As `as=s+h`, we have `h=as-s=s(a-1)`

and as `ah=a+h`, we have `ah-h=a` or `(a-1)h=a` or `h=a/(a-1)`

Hence `a/(a-1)=s(a-1)`

or `s=a/(a-1)^2`