Find the value of p so that the three lines `3x + y 2 = 0`, `p x + 2 y 3 = 0`and `2x y 3 = 0`may intersect at one point.

Explanation

Given lines, `3x+y-2=0`….`(1)`
`px+2y-3=0`……`(2)`
`2x-y-3=0`…….`(3)`
Solving equations `(1)` and `(3)`,
`x=1`, `y=-1`
`implies` Point of intersection of line `(1)` and `(3)` is `(1,-1)`
` :'` Three lines are concurrent.
`:. (1,-1)` lines on line `(2)`.
Therefore, from equation `(2)`
`p(1)+2(-1)-3=0`
`implies p=5`