Question

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

Answer 1

For the system to have infinitely many solutions, lines must coincide each other

$\Rightarrow$ratio of respective coefficients must be equal (x, y and constant coefficients)

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

Equate first two equations ;

$\Rightarrow 4k+2=3k+6$

$\Rightarrow k=4$