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