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
