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Question
If `2 /x + 3/y = 9/(xy) and 4/x + 9/y = 21/(xy)` find the values of x and y.
Solution
The given pair of equation is
`2/x + 3/y = 9/ (xy)` ………(i)
` 4/x + 9/y = 21/(xy)` ………(ii)
Multiplying (i) and (ii) by xy, we have
3x + 2y = 9 ……….(iii)
9x + 4y = 21 ………(iv)
Now, multiplying (iii) by 2 and subtracting from (iv), we get
9x – 6x = 21 – 18 ⇒ x = `3/3`= 1
Putting x = 1 in (iii), we have
3 × 1 + 2y = 9 ⇒ y = `(9−3)/2`= 3
Hence, x = 1 and y = 3.
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