Question

Find the value of k when 2x + 3y + k = 0​

Answer 1

Answer:

Step-by-step explanation:

Given lines 2x – 3y + k = 0 …i

3x – 4y – 13 = 0 …ii

8x – 11y – 33 = 0 …iii

For these lines to be concurrent, \(\begin{vmatrix} a_{1} & b_{1}&c_{1}\\ a_{2}& b_{2} & c_{2}\\ a_{3}& b_{3} & c_{3} \end{vmatrix} = 0\)

=> \(\begin{vmatrix} 2 & -3 &k \\ 3 & -4 & -13\\ 8 &-11 & -33 \end{vmatrix} = 0\)

=> 2132–143 + 3−99+104 + k−33+32 = 0

=> -22 + 15 – k = 0

=> k = -7