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Question
Find the value of k for which the following system of equations has a unique solution:
kx + 3y = 3
12x + ky = 6
Solution
kx + 3y = 3
12x + ky = 6
For no solution `a_1/a_2 - b_1/b_2 != c_1/c_2`
`=> k/12 = 2/k != 3/6`
`k/12 = 3/k`
`k^2 = 36`
`k = +- 6` i.e k = 6, -6
Also
`3/k != 3/6`
`(3 xx 6)/3 != k`
`k != 6`
k = -6 satisfies both the condition
Hence k = -6
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