Question

The value of k, for which equation 3x + 5y = 0 and kx + 10y + 0 has non-zeo solution is

(a) 6
(b) 0
(c) 2
(d) 5

Answer 1

The given system is

3x + 5y = 0 ……(i)

kx + 10y = 0 ……(ii)

This is a homogeneous system of linear differential equation, so it always has a zero solution i.e., x = y = 0.

But to have a non-zero solution, it must have infinitely many solutions.

For this, we have

$\frac{a1}{a2} = \frac{b1}{b2} \\ = > \frac{3}{k} = \frac{5}{10} = \frac{1}{2} \\ = > k = 6$

Hence, (a)6 is right..

ItzDopeGirl❣

Answer 2

Answer:

k=6

Step-by-step explanation:

This is a homogeneous system of linear differential equation,so it always has a zero solution .i.e.,x=y=0.But to have a non-zero solution,it must have infinitely many solutions.Hence,k=6