Find the value of `lambda`,if the lines`3x-4y-13=0,8x-11 y-33=0 and 2x-3y+lambda=0` are concurrent.

Explanation

The given lines are concurrent if
`|{:(3,-4,13),(8,-11,-33),(2,-3,lambda):}| = 0`
`" or " 3(-11lambda-99) +4(8lambda+66)-13(-24+22)=0`
` " or " -lambda-7=0`
`" or " lambda=-7`
Alternative method:
The given equations are
`3x-4y-13=0 " " (1)`
`8x-11y-33=0 " " (2)`
`" and " 2x-3y+lambda=0 " " (3)`
Solving (1) and (2), we get
x =11 and y=5
Thus, (11,5) is the point of intersection of (1) and (2).
The given lines will be concurrent if they pass through a common point, i.e., the point of intersection of any two lines lies on the third.
Therefore, (11,5) lies on (3), i.e.,
`2 xx 11-3 xx 5+lambda=0`
`" or " lambda=-7`