Question

The pair of linear equations 2x + 5y = k, kx + 15y = 18 has infinitely many solutions if the value of
k is

(a)3 (b) 6 (c) 9 (d) 18​

Answer 1

a1/a2=2/k ,

b1/b2=5/15,c1/c2=-k/18

2/k=5/15

30=5k

k=6

Answer 2

Answer:

k = 6

Step-by-step explanation:

Given :

2 x + 5 y =  k

2 x + 5 y - k = 0 ... ( i )

k x + 15 y = 18

k x + 15 y - 18 = 0 ........( ii )

Both equation have infinitely many solutions .

We  know formula for infinitely many solutions

$\large \dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}= \dfrac{c_1}{c_2}$

Comparing values frim ( i ) and ( ii ) we have

$\large \text{ a_1=2 \ b_1=5 \ c_1=-k and a_2=k \ b_1=15 \ c_2=-18 }$

putting these values in formula we get

$\large \dfrac{2}{-k}=\dfrac{5}{15}= \dfrac{-k}{-18}\\\\\\\large \dfrac{5}{15}= \dfrac{-k}{-18}\\\\\\\large \dfrac{1}{3}= \dfrac{k}{18}\\\\\\\large 3k=18\\\\\\\large k=6$

Thus we get answer k = 6.