Question

for what value of k do the equation 3x-y+8=0 and 6x-ky+16=0 represent the coincident lines​

Answer 1

Answer:

The value of k is 2.

Step-by-step explanation:

Pairs of linear equations are of the form:

$a_1x+b_1y+c_1=0\\a_2x+b_2y+c_2=0$

When two linear equations represent coincident lines,

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

The ratio of the coefficients of x and y and constants to the other pair is equal.

Hence, for the pair of equations in the question:   $3x-y+8=0$

and $6x-ky+16=0$

$\frac{3}{6}=\frac{-1}{-k}=\frac{8}{16}$

Therefore, $\frac{1}{2}=\frac{1}{k}$

And, k=2.

Hope it helps.