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)s=5a26+a2 and (2) s=a/(a-1)^2s=a(a1)2

Explanation:

As we have three variables a,sa,s andhh, we eliminate hh to get ss in terms of aa only.

(1) As 3s-ah=a^23sah=a2, ah=3s-a^2ah=3sa2 and h=3s/a-ah=3saa

and as as+2h=3aas+2h=3a, 2h=3a-as2h=3aas and h=3/2a-(as)/2h=32aas2

hence 3s/a-a=3/2a-(as)/23saa=32aas2

and multiplying each term by 2a2a, we get

6s-2a^2=3a^2-a^2s6s2a2=3a2a2s

or s(6+a^2)=5a^2s(6+a2)=5a2 or s=(5a^2)/(6+a^2)s=5a26+a2

(2)As as=s+has=s+h, we have h=as-s=s(a-1)h=ass=s(a1)

and as ah=a+hah=a+h, we have ah-h=aahh=a or (a-1)h=a(a1)h=a or h=a/(a-1)h=aa1

Hence a/(a-1)=s(a-1)aa1=s(a1)

or s=a/(a-1)^2s=a(a1)2