Question

4x-3y-7=0, 2x+py+2=0, 6x+4y-1=0 concurrent eqation

Answer 1

To find : p

Since lines are concurrent so they must pass through a common point .

4x-3y-7=0___________(1)

2x+py+2=0___________(2)

6x+4y-1=0 ____________(3)

concurrent eqations.

For finding point of intersection :

We subtract (1)×3 & (3)×2 ; we get

(4x-3y-7)×3 - (6x+4y-1)×2 = 0

or, 12x-9y-21 -12x-8y+2 = 0

or, -17y = 19

or, y = - 19/17

Putting y = - 19/17 in (1)

we get , 4x -3(-19/17) -7 =0

or, 4x = 7 -57/17 = 119-57 /17 = 62/17

so, x = 62/17

Hence, point of intersection of line (1) & (3)

is (62/17 , -19/17)

and as all three lines are concurrent so (2)

must satisfy this point too

so, 2x+py+2=0

or, 2(62/17) + p(-19/17) + 2 = 0

or, 124/17 -19p/17 + 34/17 = 0

or, 158-19p = 0

or, p = 158/19