Question

Find the value of $k$ for which the following system of linear equation becomes infinitely many solution or represent the coincident lines.
$6x+3y=k-3$; $2kx+6y=k$

• A. k = 5
• B. k = 2
• C. k = 6
• D. k = 3

Answer 1

The correct option is C k = 6

The given equations are
6x+3y$=$k3
2kx+6y$=$k
For infinite solution
$\frac{a1}{a2}=\frac{b1}{b2}=\frac{c1}{c2}$
we have a1$=$6.b1$=$3,c1$=$k-3
a2$=$2k,b2$=$6,c2$=$k
$\frac{6}{2k}=\frac{3}{6}=\frac{k-3}{k}$
$\frac{6}{2k}=\frac{3}{6}$
k$=$6
$\frac{3}{6}=\frac{k-3}{k}$
3k$=$6k18
3k$=$18
k=6
For k=6, given system of equation will have infinite sol.