Question

Find the value of $k$ for which each of the following systems of equations have infinitely many solution:
$kx+3y=2k+1$
$2(k+1)x+9y=7k+1$

Answer 1

For the system of equations to have infinitely many solutions, the lines must coincide.

$\Rightarrow$The ratio of corresponding coefficients must be equal.

$\Rightarrow \frac{k}{2(k+1)}=\frac{3}{9}=\frac{2k+1}{7k+1}$

Equation 1st and 2nd equality ;

$\Rightarrow 9k=6(k+1)$

$\Rightarrow k=2$