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Question
Solve the following pairs of equations by reducing them to a pair of linear equations
6x + 3y = 6xy
2x + 4y = 5xy
Solution
6x + 3y = 6xy
`⇒ (6x)/(xy) + (3y)/(xy) = 6`
`⇒ 6/y + 3/x = 6 ... (i)`
2x + 4y = 5xy
⇒ `(2x)/(xy) + (4y)/(xy) = 5`
`⇒ 2/y + 4/x = 5 ... (ii)`
Putting 1/x = p and 1/y = q in (i) and (ii) we get,
6q + 3p - 6 = 0
2q + 4p - 5 = 0
By cross multiplication method, we get
`p/(-30-(-12)) = q/(-24-(-15)) = 1/(6-24)`
`p/-18 = q/-9 = 1/-18`
`p/-18 = 1/-18 `
p = 1 and q = 1/2
p = 1/x = 1 and q = 1/y = 1/2
x = 1, y = 2
Hence, x = 1 and y = 2
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