Question

The value of $k$ for which the system of equations
$2x+3y=5$
$4x+ky=10$
has an infinite number of solutions, is ________.

• A. $1$
• B. $3$
• C. $6$
• D. $0$

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 infinitely many solutions, the condition to be satisfied is

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

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

Hence, solving this we get for $k=6$ all the conditions are satisfied, hence both the equations become same.

Therefore, infinite number of solutions.