Question

The value of $k$ for which the following system of equations has infinitely many solutions
$5x+2y=k$
$10x+4y=3$

• A. $\frac{1}{2}$
• B. $3$
• C. $\frac{3}{2}$
• D. $1$

Answer 1

Answer: (C)

$\frac{3}{2}$

For infinitely many solutions, both equations need to be identical in the ratios
i.e.
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
where, $a_1,b_1,c_1$ are the coefficients of a equation
and $a_2,b_2,c_2$ are the coefficients of another equation
Thus from
$5x+2y=k$
$10x+4y=3$
To have infinitely many solutions
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
$\frac{5}{10}=\frac{2}{4}=\frac{k}{3}$
Taking
$\frac{2}{4}=\frac{k}{3}$
$\Rightarrow \frac{1}{2}=\frac{k}{3}$

Thus,$2k=3$

$\Rightarrow k=\frac{3}{2}$ is the required answer.