Question

The pair of linear equations $2x+5y=k$ and $kx+15y=18$ has infinitely many solutions if

• A. k = 3
• B. k = 6
• C. k = 9
• D. k = 18

Answer 1

The correct option is B k = 6

The given pair of linear equations can be written in their standard form as
$2x+5y-k=0$ and $kx+15y-18=0$

On comparing it with $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$, we get

Here $a_1=2,b_1=5,c_1=-k$
$a_2=k,b_2=15,c_2=-18$

The given pair of linear equations has infinitely many solutions if

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

On substituting values we get

$\frac{2}{k}=\frac{5}{15}=\frac{-k}{-18}$

$\Rightarrow \frac{2}{k}=\frac{1}{3}=\frac{k}{18}$

$\Rightarrow k=6$

$\therefore$ The given pair of linear equations has infinite solutions when k = 6.