Question

find the value of k such that equations-x+3y-3=0 and-3x+ky-9=0,represent coincident lines

Answer 1

coincident lines means infinitely many solution,for which condition of coefficient is
$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2} \\ \frac{1}{ - 3} = \frac{3}{k} = \frac{ - 3}{ - 9} \\ from \: first \: two \: ratio \\ k = - 9 \\ from \: last \: two \: ratios \\ - 3k = - 27 \\ k = 9$
there is some problem of sign,in last term k= -9