Solve for ` x and y ` :
` 6x + 3y = 7xy, 3x + 9y = 11 xy (x ne 0 , y ne 0 )`

Options

A. `(2,2)`
B. `(3/2, 1)`
C. `(2,3)`
D. `(1, 3/2)`

Answer

D

Explanation

On dividing each of the given equations by xy, we get
` ( 6)/(y) + (3)/(x) = 7 " " ` … (i)
` (3)/( y ) + ( 9)/(x) = 11 " " `… (ii)
Putting ` (1)/(x) = u and (1)/(y) = v ` in (i) and (ii), we get
` 6v + 3u = 7 " " `... (iii)
` 3v + 9 u = 11 " "` ... (iv)
Multiplying (iii) by 3 and subtracting (iv) from the result, we get
` 18 v - 3 v = 21 - 11 `
`rArr 15 v = 10`
`rArr v = (10)/( 15) = (2)/(3)`
Putting ` v = (2)/(3)` in (iii), we get
` ( 6 xx (2)/(3)) + 3u = 7 rArr 4 + 3u = 7 rArr 3u = 3 rArr u = 1 `
Now, ` u = 1 rArr (1)/(x) = 1 rArr x = 1 `
And, ` v = (2)/(3) rArr (1)/(y) = (2)/(3) rArr 2 y = 3 rArr y = (3)/(2)`
Hence, ` x = 1 and y = (3)/(2)`.