Question

If the line 4x+3y-1=0, x-y+5=0 and Kx+5y-3=0 are concurrent the K=?

Answer 1

Let L₁​ ≡ 4x+3y−1=0; L₂ ​≡ x−y+5=0; L₃ ​≡ kx+5y−3=0

Solving equation L₁​ and L₂​ we their point of intersection which will be satisfied by L₃​ also.

Since the 3 lines are concurrent.

4x+3y=1  -(i)

x−y=−5  -(ii)

Adding (i) & (ii)

7x=−14x=−2

−2−y=−5

⇒ y=−2+5=3 

x=−2,y=3

Putting this in L₃​

kx+5y−3=0

⇒−2k+15−3=0

⇒−2k=−12k=6