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Solve the following system of equatio...

Solve the following system of equations: `2/x+3/y=9/(x y),\ \ \ 4/x+9/y=(21)/(x y),\ \ ` where `x!=0,\ y!=0`

Text Solution

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Multiplying each equation throughout by xy, we get
` 2y + 3x = 9 " " `… (i)
`4y + 9x = 21 " " `… ( ii)
Multiplying (i) by 3 and subtracting (ii) from the result, we get
` ( 6- 4 ) y = ( 27 - 21 ) rArr 2y = 6 rArr y = 3 `.
Putting ` y = 3 ` in (i), we get
` (2 xx 3) + 3x = 9 rArr 6 + 3x = 9 rArr 3x = 3 rArr x= 1 `
Hence, ` x = 1 and y = 3`.
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