Find the value of k so that the lines 3x – y – 2 = 0, 5x + ky – 3 = 0 and 2x + y – 3 = 0 are concurrent.

Given that 3x – y – 2 = 0,

5x + ky – 3 = 0


and 2x + y – 3 = 0 are concurrent


We know that,


The lines a1x + b1y + c1 = 0, a1x + b1y + c1 = 0 and a1x + b1y + c1 = 0 are concurrent if



It is given that the given lines are concurrent.



Now, expanding along first row, we get


3[(k)(-3) – (-3)(1)] – (-1)[(5)(-3) – (-3)(2)] + (-2)[5 – 2k] = 0


3[-3k + 3] + 1[-15 + 6] – 2[5 – 2k] = 0


-9k + 9 – 9 – 10 + 4k = 0


-5k – 10 = 0


-5k = 10


k = -2


Hence, the value of k = -2


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