Question

The value of $k$ for which the system of equations $3x+5y=0$ and $kx+10y=0$ has a non-zero solution, is ________.

• A. $0$
• B. $2$
• C. $6$
• D. $8$

Answer 1

Answer: (C)

$6$

For a system of equations $a_{1}x+b_{1}y+c_1=0;a_{2}x+b_{2}y+c_2=0$ to have non-zero solutions, the condition to be satisfied is

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

$\therefore \frac{3}{k}=\frac{5}{10}$

or $k=6$