Question

find the value of x and y if the equations kx + 4y=k_4, 16x+ky =k has infinitely many solutions

Answer 1

hello,
compare the set of equations with a₁x+b₁y+c₁=0   a₂x+b₂y+c₂=0
a₁=k,b₁=4,c₁=-(k-4)
a₂=16,b₂=k,c₂=-k
for infinitely many solutions
a₁/a₂=b₁/b₂=c₁/c₂
k/16=4/k=-(k-4)/-k
1st-k/16=4/k
k²=64
k=8 or -8
2nd-4/k=(k-4)/k
4=k-4
k=8
∴for k=8 the set of equations have infinitely many solutions

@skb

Answer 2

For infinite many solutions

$\frac{a_{1} }{ a_{2} } = \frac{ b_{1} }{ b_{2}} = \frac{ c_{1} }{ c_{2} }$

$\frac{k}{16} = \frac{4}{k} = \frac{k-4}{k}$

from
$\frac{k}{16} = \frac{4}{k}$

$k^{2}=16*4=64$

$k=8$

#Prashant24IITBHU