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Question
Find the values of k for which the system of equations 3x + ky = 0,
2x – y = 0 has a unique solution.
Solution
The given pair of linear equations are
3x + ky = 0 ……(i)
2x – y = 0 ……(ii)
Which is of the form `a_1x + b_1y + c_1 = 0 and a_2x + b_2y + c_2 = 0`, where
`a_1 = 3, b_1 = k, c_1 = 0, a_2 = 2, b_2 = -1 and c_2 = 0`
For the system to have a unique solution, we must have
`(a_1)/(a_2) = (b_1)/(b_2)`
`⇒ 3/2 ≠ k/(−1)`
`⇒ k ≠ – 3/2`
Hence,` k ≠ – 3/2.`
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