Question

The value of $k$ for which the following system of equations has infinitely many solutions
$2x-ky+3=0$
$3x+2y-1=0$

• A. $\frac{1}{3}$
• B. $\frac{-2}{3}$
• C. $\frac{3}{2}$
• D. $\frac{-4}{3}$

Answer 1

The correct option is D $\frac{-4}{3}$

For no solution, the equations should differ only is constant
Rewrite
$2x-ky=-3$
$3x+2y=+1$
now put the options for $k$ and check if the LHS of both the equations are identical
We find that $k=\frac{-4}{3}$ makes the LHS of both equations same