Question

The pair of linear equations $(3k+1)x+3y-5=0$ and $2x-3y+5=0$ have infinite solutions. Then the value of $k$ is:

• A. $1$
• B. $0$
• C. $2$
• D. $-1$

Answer 1

The correct option is D $-1$

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

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

$\Rightarrow \frac{3k+1}{2}$$=\frac{3}{-3}$$=\frac{5}{-5}$

$\Rightarrow 3k+1=-2$

$\Rightarrow 3k=-3$

$\Rightarrow k=-1$