Find the value of k for which the system 3x + 5 = 0, kx + 10y = 0 has a nonzero solution.
The given two equations are:
3x + 5y = 0 …(i)
kx + 10y = 0 …(ii)
The given equation is a homogenous system of linear differential equation so it always has a zero solution
We know that, for having a non – zero solution it must have infinitely many solutions
∴
k = 6
Hence, the value of k is 6