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.

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Answer 1 · 2018-01-22T06:13:22

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

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 $s=a/(a-1)^2$