Question

Solve for ` x and y ` :
` ( 3a)/(x) - ( 2b )/(y ) + 5 = 0, (a)/(x) + ( 3b)/( y) - 2 = 0 ( x ne 0 , y ne 0 )`

Answer 1

Putting ` (1)/(x) = u and (1)/(y) = v `, the given equations become
` 3au - 2 bv = - 5" " `… (i)
` au + 3 bv = 2" "`… (ii)
Multiplying (ii) by and substracting (i) from the result, we get
` 9bv + 2 bv = 6 + 5`
` rArr 11bv = 11 rArr v = (11)/(11 b ) = (1)/(b)`
Putting ` v = (1)/(b) ` in (ii), we get
`au + 3= 2 rArr au = - 1 rArr u = (-1)/(a)`
Now, `u = (-1)/(a) rArr (1)/(x) = (-1)/(a) rArr - x = a rArr x = - a `
And, ` v = (1)/(b) rArr (1)/(y) = (1)/(b) rArr y = b ` .
Hence,` x = - a and y = - b `