Q. 214.4( 7 Votes )
Solve for x and y:
Answer :
We have
and 
where x≠0 and y≠0
Lets simplify these equations. Assuming 1/x = p and 1/y = q, we can rewrite them,
⇒ 3p – q = - 9 …(i)
⇒ 2p + 3q = 5 …(ii)
To solve these equations, we need to make one of the variables (in both the equations) have same coefficient.
Lets multiply eq.(i) by 3, so that variable q in both the equations have same coefficient.
Recalling equations (i) & (ii),
3p – q = - 9 [×3
2p + 3q = 5
⇒ 11p = - 22
⇒ p = - 2
Substitute p = - 2 in eq.(i)/eq.(ii), as per convenience of solving.
Thus, substituting in eq.(i), we get
3( - 2) – q = - 9
⇒ - 6 – q = - 9
⇒ q = 9 – 6
⇒ q = 3
Thus, p = - 2 and q = 3
As p = 1/x,
⇒ - 2 = 1/x
⇒ x = - 1/2
And q = 1/y
⇒ 3 = 1/y
⇒ y = 1/3
Hence, we have x = - 1/2 and y = 1/3
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