Question

What value of K, will the following pair of the linear equations have infinitely many solutions?
$2x+3y-13=0;6x-ky-39=0$

Answer 1

We have,

$2x+3y-13=0$ $..........\left(1\right)$

$6x-ky-39=0$ $..........\left(2\right)$

Since, linear equations have infinitely many solution.

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Therefore,

$\frac{2}{6}=\frac{3}{-k}=\frac{-13}{-39}$

$\frac{1}{3}=\frac{3}{-k}$

$\therefore k=-9$