Question

Find the value of k for which the system of equations 3x + 5y = 0 and kx + 10y = 0 has infinite nonzero solutions.

Find the value of k for which the system 3x + 5y = 0, kx + 10y = 0 has a nonzero solution.

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

`(a_1)/(a_2) = (b_1)/(b_2)`

⇒ `3/k = 5/10 = 1/2`

⇒ k = 6

Hence, k = 6.