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Question
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
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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