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Question
Find the value of k for which the system of equations has a unique solution:
5x – 7y = 5,
2x + ky = 1.
Solution
The given system of equations are
5x - 7y – 5 = 0 ….(i)
2x + ky - 1 = 0 …(ii)
This system is of the form:
`a_1x+b_1y+c_1 = 0`
`a_2x+b_2y+c_2 = 0`
where,` a_1 = 5, b_1= -7, c_1= -5 and a_2 = 2, b_2 = k, c_2= -1`
Now, for the given system of equations to have a unique solution, we must have:
`(a_1)/(a_2)≠ (b_1)/(b_2)`
`⇒ 5/2 ≠ (−7)/k`
`⇒ k ≠ - 14/5`
Hence`k≠ - 14/5`
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