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.

1 Answer
Jan 22, 2018

(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#