Question

For what value of k, the pair of linear equations $3x+ky=9$ and $6x+4y=18$ has infinitely many solutions?

• A. -5
• B. 6
• C. 1
• D. 2

Answer 1

The correct option is D

2

Given equations gives infinitely many solutions if,
$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

The given linear equations are:
$3x+ky=9;6x+4y=18.$
$\Rightarrow a_1=3,b_1=k,c_1=-9$ and $a_2=6,b_2=4,c_2=-18$

$\Rightarrow \frac{3}{6}=\frac{k}{4}=\frac{-9}{-18}$

$\Rightarrow \frac{1}{2}=\frac{k}{4}$

$\Rightarrow k=2$