Question

find the value of k for which system of linear equation x minus Y is equal to zero and 2 X + K Y is equal to zero has non zero solution​

Answer 1

$x - y = 0 .........(i) \\ x = y.......(ii)\\ 2x + k = y.......(iii) \\ put \: the \: value \: of \: x \: in \: equation \: (iii) \\ 2x + y = k......(iii) \\ 2y + k = y \\ k = - y \\ now \: put \: the \: value \: of \: k \: and \: x \: in \: equation \: (iii) \\ 2x + k = y........(iii) \\ 2y + ( - y) = y \\ 2y - y = y \\ y = y = (0) \\ hence \: (x =y = 0) \: (y = 0) \: (k = - y = 0)$