Question

The value of $k$ for which the system of equations $x+2y-3=0$ and $5x+ky+7=0$ has no solution, is ________.

• A. $10$
• B. $6$
• C. $3$
• D. $1$

Answer 1

The correct option is A $10$

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 no solution, the condition to be satisfied is

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

$\Rightarrow \frac{1}{5}=\frac{2}{k}\ne \frac{-3}{7}$

$\therefore$ For $k=10$, the given system of equation has no solution.