Question

linear eqn 5x+(k-4)y-20=0 and 3x+(k+7)y-12=0 has infinitely many soln then k is

Answer 1

linear pair of equations with variables have
infinite solution if

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}$
as a1x+b1y+c1 is the form of first equation and a2x+b2y+c2 is the second equation


therefore

$\frac{5}{3 } = \frac{k - 4}{k - 7 } = \frac{ - 20}{ - 12}$
then

$5(k - 7) = 3(k - 4)$
$5k - 35 = 3k - 12$
$2k = 23$
$k = 12.5$