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Solve the following pairs of equations by reducing them to a pair of linear equations 6x + 3y = 6xy, 2x + 4y = 5xy - Mathematics

Solve the following pairs of equations by reducing them to a pair of linear equations

6x + 3y = 6xy

2x + 4y = 5xy

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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

  Is there an error in this question or solution?
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APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.6 | Q 1.6 | Page 67
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