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