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)2
C)6
D)1​

Answer 1

option ( b ) is ✅ correct

Step by step explanation is above there

Hope it helps you

Thank you

Answer 2

Answer:

Option (B) 2 is the value of k .

Step-by-step explanation:

Explanation:

Given , 3x + ky = 9 and 6x + 4y = 18

Condition for a infinite solution - If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

Let a pair of linear equations $a_1 x^2 + b_1x+c_1$ and $a_2x^2+b_2x+c_2$  has infinitely many solution then ,

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

Step 1:

From the given equations we have ,

$a_1 = 3 , b_1 = k, c_1 = -9 \ and\ a_2 = 6 , b_2 = 4 c_2 = -18$ .

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

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

⇒12 = 6k   and -18k = -36

⇒k = 2       and k = 2 .

Final answer:

Hence , the value of k is 2  .

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