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Find the value(s) of k for which the pair of equations

kx + 2y = 3

3x + 6y = 10 has a unique solution.

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#### Solution

The given equations are

kx + 2y = 3

3x + 6y = 10

For a unique solution,

`a_1/a_2 ≠ b_1/b_2`

Where a_{1}= k, a_{2 }= 3, b_{1} = 2, b_{2} = 6.

`k/3 ≠ 2/6`

⇒ k ≠ 1

For all values of k except 1, the given linear equations will have a unique solution.

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**Solution :**

Compare x^{2} + 2x – 9 = 0 with ax^{2} + bx + c = 0

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∴ b^{2} – 4ac = (2)^{2} – 4 × `square` × `square`

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∴ b^{2} – 4ac > 0

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