Question

for what value of k , do the qquations 2x-3y= -10 , and 3x+ky= -15 represent coincident lines

Answer 1

Solution :

2x - 3y= -10

and 3x + ky= -15

$\sf\large{{a_1x_1} + {b_1y }+ {c_1} = 0}$

$\sf\large{{a_2x_2} +{ b_2y }+{ c_2 }= 0}$

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

$\sf\large{a_1}{a_2}= \frac{2}{3}$

$\sf\large{b_1}{b_2} = \frac {-3}{-k}$

$\sf\large\frac{c_1}{c_2} = \frac{10}{15}$

$\sf\large\frac{2}{3} =\frac {-3}{k}=\frac{10}{15}$

$\sf\large{k = \frac{9}{2}}$