Find the Value(S) Of K for Which the Pair of Equations Kx + 2y = 3 3x + 6y = 10 Has a Unique Solution. - Mathematics

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Sum

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 a1= k, a2 = 3, b1 = 2, b2 = 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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2018-2019 (March) 30/4/3

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Solution :

Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0

a = 1, b = 2, c = `square`

∴ b2 – 4ac = (2)2 – 4 × `square` × `square`

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