For what value of k, do the equations 3x - y | vedclass

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(D) The condition for two lines $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to be coincident is $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1

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$2$

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(D) The condition for two lines $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ to be coincident is $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$.Given equations are $3x - y + 8 = 0$ and $6x - ky + 16 = 0$.Comparing with the standard form,we have $a_1 = 3, b_1 = -1, c_1 = 8$ and $a_2 = 6, b_2 = -k, c_2 = 16$.Substituting these values into the condition:$\frac{3}{6} = \frac{-1}{-k} = \frac{8}{16}$.Simplifying the ratios:$\frac{1}{2} = \frac{1}{k} = \frac{1}{2}$.From $\frac{1}{k} = \frac{1}{2}$,we get $k = 2$.

For what value of $k,$ do the equations $3x - y + 8 = 0$ and $6x - ky = -16$ represent coincident lines?

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