1.

Solve for ` x and y ` : ` (2)/(x) + (3)/(y ) = 13, (5)/(x) - ( 4)/( y) = - 2 ( x ne 0 and y ne 0 )`

Answer» Putting ` (1)/(x) = u and (1)/(y) = v `, the given equations become
` 2u + 3 v = 13" " `… (i)
` 5u - 4 v = - 2 " " `… (ii)
Multiplying (i) by 4 and (ii) by 3 and adding the results , we get
` 8 u + 15u= 52 - 6`
` rArr 23 u = 46 `
` rArr u = ( 46)/( 23) = 2`.
Putting `u = 2 ` in (i), we get
` ( 2 xx 2 ) + 3v = 13 rArr 3 v = 13 - 4 = 9 rArr v = 3`.
Now, ` u = 2 rArr (1)/(x) 2x = 1 rArr x = (1)/(2)`
And, ` v = 3 rArr (1)/(y) = 3 rArr 3y = 1 rArr y = (1)/(3)`.
Hence, `x = (1)/(2) and y = (1)/(3)`.


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