Question

for what value of k system of equation 5x-7y-5=0 and 2x+ky-1=0 have unique solution ​

Answer 1

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Answer 2

$Compare \: given \: system \:of \: equations \\5x-7y-5=0 \: and \: 2x+ky-1=0 \:with \\a_{1}x+b_{1}y+c_{1}=0 \:and \: a_{2}x+b_{2}y+c_{2}=0 ,\\we \:get$

$a_{1} = 5 , b_{1} = -7 , \: c_{1} = -5 ;$

$and \:a_{2} = 2 , b_{2} = k , \: c_{2} = -1$

$\frac{a_{1}}{a_{2}} \neq \frac{b_{1}}{b_{2}} \\\blue{ ( Given \: equations \: have \: unique \: solution)}$

$\implies \frac{5}{2} \neq \frac{-7}{k}$

$\implies k \neq (-7) \times \frac{2}{5}$

$\implies k \neq \frac{-14}{5}$

Therefore.,

$\red{ Value \: of \: k }\green { \neq \frac{-14}{5}}$

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