for what value of k will the following pair of linear equations have no solution 2x+ky=1 6x+4y=3

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Solution

Dear Student,

$2 x + k y = 1 \Rightarrow 2 x + k y - 1 = 0 6 x + 4 y = 3 \Rightarrow 6 x + 4 y - 3 = 0 T h e s e t w o e q u a t i o n s a r e o f t h e f o r m : a_{1} x + b_{1} y + c_{1} = 0 a_{2} x + b_{2} y + c_{2} = 0 w h e r e, a_{1} = 2, b_{1} = k, c_{1} = - 1 a n d a_{2} = 6, b_{2} = 4, c_{2} = - 3 F o r t w o e q u a t i o n s t o h a v e n o s o l u t i o n : \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}} H e r e, \frac{2}{6} = \frac{k}{4} \neq \frac{- 1}{- 3} \frac{2}{6} = \frac{k}{4} k = \frac{2 \times 4}{6} k = \frac{4}{3}$

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