Question

$5x - 7y - 5 = 0 and 2x + ky - 1 = 0$
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Answer 1

$\sf\large\underline\red{Given:-}$

$\sf\ 5x-7y-5=0$

$\sf {\implies 5x-7y=5---------(i)}$

$\sf\ 2x+ky-1=0$

$\sf {\implies 2x+ky=1---------(ii)}$

From (i) & (ii) we get-

$\sf \frac{a\:_{1}}{a\:_{2}}=\frac{b\:_{1}}{b\:_{2}}=\frac{c\:_{1}}{c\:_{2}}$

$\sf {\implies \frac{5}{2}=\frac{-7}{k}=\frac{5}{1}}$

$\sf\large\underline\red{Therefore,}$

$\sf \frac{5}{2}=\frac{-7}{k}$

$\sf {\implies k=\frac{-14}{5}}$