Question

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

• A. $1$
• B. $-1$
• C. $2$
• D. $-2$

Answer 1

The correct option is D $-2$

Three lines are concurrent if they pass through a common point i.e., point of intersection of any two lines lies on the third line.

It is given that lines

$2x+y-3=0$ .......(1)

$5x+ky-3=0$ ......(2)

$3x-y-2=0$ .......(3) are concurrent.

So finding point of intersection of lines 1 and 3, we get, $(1,1)$.

Since, lines 1, 2 and 3 are concurrent.

Thus, the point will satisfy equation of line 2.

Thus,

$5\left(1\right)+k\left(1\right)-3=0$

$k+2=0$

$k=-2$