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If (2)/(x) + (3)/(y) = 6 and (1)/(x)...

If ` (2)/(x) + (3)/(y) = 6 and (1)/(x) + (1)/(2y) = 2` then

A

` x =1, y = (2)/(3)`

B

` x = (2)/(3), y = 1 `

C

` x = 1, y = (3)/(2)`

D

` x = (3)/(2), y = 1 `

Text Solution

Verified by Experts

The correct Answer is:
B
Put ` (1)/(x) = u and (1)/(y) = v`. Then ` 2u + 3 v = 6 `" "`... (i) and `u + (1)/(2) v = 2 rArr 2u + v = 4 `... (ii)
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Find the S.D. between the lines : (i) (x)/(2) = (y)/(-3) = (z)/(1) and (x -2)/(3) = (y - 1)/(-5) = (z + 4)/(2) (ii) (x -1)/(2) = (y - 2)/(3) = (z - 3)/(2) and (x + 1)/(3) = (y - 1)/(2) = (z - 1)/(5) (iii) (x + 1)/(7) = (y + 1)/(-6) = (z + 1)/(1) and (x -3)/(1) = (y -5)/(-2) = (z - 7)/(1) (iv) (x - 3)/(3) = (y - 8)/(-1) = (z-3)/(1) and (x + 3)/(-3) = (y +7)/(2) = (z -6)/(4) .

(x) / (2) + (y) / (3) = 1 (x) / (3) + (y) / (2) = 1

( 1 ) /( 2x ) + (1 ) /( 3y ) = 2, (1) /( 3x ) + (1) /( 2y ) = ( 13) /( 6) ( x ne 0 , y ne 0 )

(5) / (x-1) + (1) / (y-2) = 2 (6) / (x-1) - (3) / (y-2) = 1

Find each of the following products: (i) (x - 4)(x - 4) (ii) (2x - 3y)(2x - 3y) (iii) ((3)/(4) x - (5)/(6) y) ((3)/(4)x - (5)/(6) y) (iv) (x - (3)/(x)) (x - (3)/(x)) (v) ((1)/(3) x^(2) - 9) ((1)/(3) x^(2) - 9) (vi) ((1)/(2) y^(2) - (1)/(3) y) ((1)/(2) y^(2) - (1)/(3) y)

{:((5)/(x - 1) + (1)/(y - 2) = 2),((6)/(x - 1) - (3)/(y - 2) = 1):}

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