1. Tardigrade
  2. Question
  3. Mathematics
  4. The value of λ , for which the lines 3x - 4y =13, 8x -11y = 33 and 2x - 3y + λ = 0 are concurrent is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The value of $\lambda $ , for which the lines $3x - 4y =13, 8x -11y = 33$ and $2x - 3y + \lambda = 0$ are concurrent is

BITSATBITSAT 2014

Solution:

For concurrency of $3$ lines the determinant of coefficients of equations should be $0$.
$\begin{vmatrix}3&-4&-13\\ 8&-11&-33\\ 2&-3&\lambda\end{vmatrix} = 0 $
$ \Rightarrow 3\left(-11\lambda -99\right)+4\left(8\lambda +66\right) -13\left(-24+22\right) = 0 $
$ \Rightarrow -33\lambda - 297 + 32\lambda + 264 + 312 - 286 = 0 $
$\Rightarrow -\lambda - 583+ 576 = 0 \Rightarrow \lambda = -7$