Question

For which value K will the pair of linear equations 2x-7y=-2 ; Kx+14y=18 have no solution. ​

Answer 1

Answer:

The required value of k is 4

Answer 2

$Given \: pair \: of \: linear\: equations : \\2x - 7y = -2 \implies 2x - 7y + 2 = 0 \: ---(1) \\and \: kx + 14y = 18 \implies Kx + 14y - 18 = 0\: ---(2)$

$Compare \: above \: equations \: with \\a_{1}x + b_{1}y + c_{1} = 0 \: and \: \\a_{2}x + b_{2}y + c_{2} = 0, \: we \: get$

$a_{1} = 2 , b_{1} = -7 , c_{1} = 2 \: and \\a_{2} = K, b_{2} = 14 , c_{2} = -18$

$\boxed{\pink{ \frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}} } }$

$\blue{ ( Given \: above \: equations \: have }\\\blue{ no \: solution )}$

$\implies \frac{2}{K} = \frac{-7}{14}$

$\implies \frac{2}{K} = \frac{-1}{2}$

$\implies 2 \times \frac{ -2}{1} = K$

$\implies - 4 = K$

Therefore.,

$\red{ Value \: of \: K } \green { = -4 }$

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