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

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Solution

$D e a r s t u d e n t, f o r c o i n c i d e n t l i n e : \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} = \frac{c_{1}}{c_{2}} s o, a s p e r q u e s t i o n : 3 x - y + 8 = 0 a_{1} = 3; b_{1} = - 1; c_{1} = 8 6 x - k y = - 16 \Rightarrow 6 x - k y + 16 = 0 a_{2} = 6; b_{2} = - k; c_{2} = 16 \frac{3}{6} = \frac{- 1}{- k} = \frac{8}{16} t h e r e f o r e, \frac{1}{2} = \frac{1}{k} \Rightarrow k = 2 R e g a r d s$

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