Question

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

• A. -5
• B. 6
• C. 1
• D. 2

Answer 1

The correct option is D

2

3x+ky = 9; 6x +4y=18

Here, $a_1$=3, $b_1$=k , $c_1$=9, $a_2$=6, $b_2$=4, $c_2$=18

Given equations will have infinitely many solutions if it satisfies the condition below

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

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

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

$\Rightarrow$ k = 2