Question

The value of $k$ for which the system $kx+3y=7$ and $2x-5y=3$ has no solution is:

• A. $7$ and $k=-\frac{3}{14}$
• B. $4$ and $k=\frac{3}{14}$
• C. $\frac{6}{5}$ and $k\ne \frac{14}{3}$
• D. $-\frac{6}{5}$ and $k\ne \frac{14}{3}$

Answer 1

The correct option is D $-\frac{6}{5}$ and $k\ne \frac{14}{3}$

$kx+3y=7$
$2x-5y=3$
Here, $a_1=k_1,b_1=3,c_1=-7$
$a_2=2,b_2=-5,c_2=-3$
For no solution, $\frac{k}{2}=\frac{3}{-5}\ne \frac{-7}{-3}$
$\Rightarrow k=\frac{-6}{5}$ and $k\ne \frac{14}{3}$