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Question
Find the value of k for which the system of equations
5x - 3y = 0, 2x + ky = 0
has a non-zero solution.
Solution
The given system of equations:
5x - 3y = 0 ….(i)
2x + ky = 0 ….(ii)
These equations are of the following form:
`a_1x+b_1y+c_1 = 0, a_2x+b_2y+c_2 = 0`
where, `a_1 = 5, b_1= -3, c_1 = 0 and a_2 = 2, b_2 = k, c_2 = 0`
For a non-zero solution, we must have:
`(a_1)/(a_2) = (b_1)/(b_2)`
`⇒ 5/2 = (−3)/k`
`⇒5k = -6 ⇒ k = (−6)/5`
Hence, the required value of k is `(−6)/5`.
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