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Question
Solve the following pair of equations:
`4x + 6/y = 15, 6x - 8/y = 14, y ≠ 0`
Solution
Given pair of linear equations are
`4x + 6/y` = 15 ......(i)
And `6x - 8/y = 14, y ≠ 0` ....(ii)
Let u = `1/y`, then above equation becomes
4x + 6u = 15 .....(iii)
And 6x – 8u = 14 .....(iv)
On multiplying equation (iii) by 8 and equation (iv) by 6 and then adding both of them, we get
32x + 48u = 120
36x – 48u = 84
⇒ 68x = 204
⇒ x = 3
Now, put the value of x in equation (iii), we get
4 × 3 + 6u = 15
⇒ 6u = 15 – 12
⇒ 6u = 3
⇒ u = `1/2`
⇒ `1/y = 1/2` .....`[because u = 1/y]`
⇒ y = 2
Hence, the required values of x and y are 3 and 2, respectively.
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