Question

Find the value of $k$ for which the system of equation $x-ky=2,3x+6y=6$ have inflnitely many solutions.

Answer 1

The system of equations consist equations of two straight lines.

So, the system have infinite no. of solution if the lines are coincident.

Two lines $ax+by=c$ and $px+qy=r$ are coincident if,

$\frac{a}{p}=\frac{b}{q}=\frac{c}{r}$

For the given equations,

$\frac{1}{3}=\frac{-k}{6}=\frac{2}{6}$

$\frac{1}{3}=\frac{-k}{6}=\frac{1}{3}$

$\Rightarrow -3k=6$

$k=-2$