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If the lines 2x + y -3 = 0, 5x + k y - ...

If the lines `2x + y -3 = 0`, `5x + k y - 3 = 0` and `3x - y - 2 = 0`are concurrent, find the value of k.

Text Solution

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given that `L_1, L_2 , L_3 ` are concurrent
`L_1 = 2x+ y -3=0` eqn(1)
`L_2 = 5x + ky - 3=0` eqn(2)
`L_3 = 3x-y-2 = 0` eqn(3)
adding equations `1 & 2:`
`2x + y - 3+ 3x - y-2 = 0`
`5x- 5 = 0`
`x=1`
...
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