Question

If the pair of equations $2x+3y-5=0$ and $4x+ky-10=0$ has infinite number of solutions, then the value of $k$ is:

• A. $k=\frac{3}{2}$
• B. $k=6$
• C. $k\ne \frac{3}{2}$
• D. $k\ne 6$

Answer 1

The correct option is B $k=6$

For the two lines $a_{1}x+b_{1}y-c_1=0$ and$a_{2}x+b_{2}y-c_2=0$ to have infinite solutions,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

Here, the lines are $2x+3y-5=0$ and $4x+ky-10=0$

Thus, $\frac{2}{4}=\frac{k}{3}=\frac{5}{10}$

$\Rightarrow k=6$