Question

If the given pair of equations has infinitely many solutions, then find the value of $k$ ?

$2x+4y=k$

$6x+12y=9$

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

A pair of linear equations,
$a_{1}x+b_{1}y=c_1$
$a_{2}x+b_{2}y=c_2$
are said to have infinitely many solutions if
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

We have,

$2x+4y=k$

$6x+12y=9$

Here, $a_1=2,b_1=4,c_1=k$ and $a_2=6,b_2=12,c_2=9$

For infinitely many solutions, $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

$\Rightarrow \frac{2}{6}=\frac{4}{12}=\frac{k}{9}$

$\Rightarrow \frac{2}{6}=\frac{k}{9}$

$\Rightarrow \frac{1}{3}=\frac{k}{9}$

$\Rightarrow k=\frac{9}{3}$

$\therefore k=3$