1.

Solve for ` x and y ` : ` (1)/( 7x ) + ( 1) /( 6y) = 3, (1)/( 2x) - (1)/( 3y ) = 5 (x ne 0, y ne 0)`

Answer» Putting `(1)/(x) = u and (1) /( y) = v ` , the given equations become
` (u)/( 7) + (v)/( 6) = 3 rArr 6u + 7v = 126 " " ` … (i)
` (u)/(2 ) - (v)/( 3) = 5 rArr 3u - 2v = 30 " " `… (ii)
Multiplying (i) by 2 and (ii) by 7 and adding the results, we get
` 12 u + 21 u = 252 + 210 `
` rArr 33u = 462 `
` rArr u = ( 462 )/(33) = 14 `
Putting `u = 14 `in (i), we get
` ( 6xx 14) + 7v = 126`
` rArr 7v = 126 - 84 = 42 rArr v = ( 42 )/(7) = 6`
Now, ` u = 14 rArr (1)/(x) = 14 rArr 14 x = 1 rArr x = (1)/( 14)`
And ,` v = 6 rArr (1)/(y) = 6 rArr 6y = 1 rArr y = (1)/(6)`.
Hence, ` x = (1)/( 14) and y = (1)/( 16 )`


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