Question

Solve :
`3/(2x) + 2/(3y) = -1/3`

`3/(4x) + 1/(2y) = -1/8`

Answer 1

Given equations are `3/(2x) + 2/(3y) = -1/3 and 3/(4x) + 1/(2y) = -1/8`

Let `1/x = u and 1/y = v`
Then, the system of equations become
`3/2u + 2/3v = -1/3  and 3/4u + 1/2v = -1/8`

⇒ `[ 9u + 4v ]/6 = -1/3 and  [ 3u + 2v ]/4 = -1/8`

⇒ 27u + 12v = -6 and 24u + 16v = -4
⇒ 27u + 12v + 6 = 0 and 24u + 16v + 4 = 0

⇒ `u/[ 12 xx 4 - 16 xx 6 ] = (- v)/[ 27 xx 4 - 24 xx 6 ] = 1/[ 27 xx 16 - 24 xx 12 ]`

⇒ `u/[ 48 - 96 ] = (- v)/[ 108 - 144 ] = 1/[ 432 - 288 ]`

⇒ `u/[ -48 ] = (- v)/[ - 36 ] = 1/[ 144 ]`

⇒ `u/[ -48 ] = ( v)/[ 36 ] = 1/[ 144 ]`

⇒ `u = [ -48 ]/144 = 1/3  and v = 36/144 = 1/4 `

⇒ `1/x = - 1/3 and 1/y = 1/4`

⇒ x = - 3 and y = 4.